A One Ampere Current Is Over Six Billion Billion Electrons a Second
Calculate charge, current and time from I = Q/t, find the work done in moving a charge through a potential difference, draw a circuit with the standard symbols, and read a resistance off a V-I graph.
What is actually moving when a current flows?
Switch on a bulb and it lights immediately, which makes it tempting to think something has travelled from the switch to the bulb at enormous speed. Nothing of the sort has happened. The electrons were already in the wire all along, spread through it like water already filling a pipe, and closing the switch simply set them all drifting at once.
What we call an electric current is that drift — a flow of charge through a conductor. And because charge comes in extremely small units, an ordinary current involves a staggering number of them:
So a current of one ampere means about six billion billion electrons passing a point every second.
Three quantities describe every circuit, and this part of the chapter defines each one precisely:
- Current — how much charge flows per second
- Potential difference — how much energy each unit of charge carries
- Resistance — how much the conductor opposes the flow
And one relation connects all three, which is why a single equation can predict the behaviour of a circuit you have never built.
This page covers the first part of the CBSE Class 10 Science chapter on electricity: current and charge, potential difference, circuit diagrams, and Ohm's law with the V-I graph.
What we call an electric current is that drift — a flow of charge through a conductor. And because charge comes in extremely small units, an ordinary current involves a staggering number of them:
So a current of one ampere means about six billion billion electrons passing a point every second.
Three quantities describe every circuit, and this part of the chapter defines each one precisely:
- Current — how much charge flows per second
- Potential difference — how much energy each unit of charge carries
- Resistance — how much the conductor opposes the flow
And one relation connects all three, which is why a single equation can predict the behaviour of a circuit you have never built.
This page covers the first part of the CBSE Class 10 Science chapter on electricity: current and charge, potential difference, circuit diagrams, and Ohm's law with the V-I graph.
How do you calculate current, charge or time?
Current is the charge passing a point divided by the time taken.
where is in amperes (A), in coulombs (C) and in seconds (s).
The definition of the ampere follows from it. One ampere is one coulomb per second:
Worked example 1. A charge of C flows through a conductor in s. Find the current.
Worked example 2. A current of A flows for minutes. How much charge has passed?
Convert the time to seconds first: minutes s.
The conversion is compulsory. Using instead of gives C, which is sixty times too small — and time in minutes is the single commonest slip in these numericals.
Worked example 3 — counting the electrons. How many electrons pass through the conductor in worked example 1?
Each electron carries C, so
Worked example 4. How long does a A current take to deliver C?
One direction that has to be stated carefully. Current is taken to flow from the positive terminal to the negative terminal outside the cell — that is conventional current. But the particles actually moving in a metal are electrons, which are negative and therefore drift the opposite way.
So the current and the electrons go in opposite directions, and both statements are correct because they describe different things. A question asking the direction of current wants positive to negative; one asking the direction of electron flow wants the reverse.
How current is measured. An ammeter is connected in series, so that the whole current passes through it, and it must have a very low resistance so that inserting it does not change the current it is trying to measure. An ammeter connected in parallel would short out the component, which is why the connection is part of the definition.
where is in amperes (A), in coulombs (C) and in seconds (s).
The definition of the ampere follows from it. One ampere is one coulomb per second:
Worked example 1. A charge of C flows through a conductor in s. Find the current.
Worked example 2. A current of A flows for minutes. How much charge has passed?
Convert the time to seconds first: minutes s.
The conversion is compulsory. Using instead of gives C, which is sixty times too small — and time in minutes is the single commonest slip in these numericals.
Worked example 3 — counting the electrons. How many electrons pass through the conductor in worked example 1?
Each electron carries C, so
Worked example 4. How long does a A current take to deliver C?
One direction that has to be stated carefully. Current is taken to flow from the positive terminal to the negative terminal outside the cell — that is conventional current. But the particles actually moving in a metal are electrons, which are negative and therefore drift the opposite way.
So the current and the electrons go in opposite directions, and both statements are correct because they describe different things. A question asking the direction of current wants positive to negative; one asking the direction of electron flow wants the reverse.
How current is measured. An ammeter is connected in series, so that the whole current passes through it, and it must have a very low resistance so that inserting it does not change the current it is trying to measure. An ammeter connected in parallel would short out the component, which is why the connection is part of the definition.
What does potential difference mean, and how do you find the work done?
Potential difference is the work done in moving a unit charge from one point to the other.
where is in volts (V), in joules (J) and in coulombs (C).
And that gives the definition of the volt. One volt is one joule per coulomb:
**So a V battery does not mean twelve of something. It means that every coulomb of charge passing through the circuit carries joules of energy with it — energy the battery supplied and the circuit will use up.
Worked example 1.** How much work is done in moving a charge of C through a potential difference of V?
Worked example 2. A V battery drives C round a circuit. How much energy has it supplied?
Worked example 3 — working backwards. J of work moves a charge of C between two points. Find the potential difference.
Worked example 4 — combining the two relations. A current of A flows for s through a V source. How much energy is used?
Notice that the two formulas chain together naturally, and that chain is the whole of the energy calculation you will meet again in Part 3.
Why a potential difference is needed at all. Electrons will not drift on their own; something has to keep pushing them. A cell maintains a potential difference across the circuit, which is what keeps the charge moving — and the moment the cell is exhausted, the difference disappears and the current stops.
How potential difference is measured. A voltmeter is connected in parallel across the two points, and it must have a very high resistance so that almost no current is diverted into it.
So the two meters are connected in opposite ways for opposite reasons. The ammeter goes in series and has low resistance; the voltmeter goes in parallel and has high resistance. Each is designed not to disturb the quantity it measures, and swapping their connections is a standard examination trap.
where is in volts (V), in joules (J) and in coulombs (C).
And that gives the definition of the volt. One volt is one joule per coulomb:
**So a V battery does not mean twelve of something. It means that every coulomb of charge passing through the circuit carries joules of energy with it — energy the battery supplied and the circuit will use up.
Worked example 1.** How much work is done in moving a charge of C through a potential difference of V?
Worked example 2. A V battery drives C round a circuit. How much energy has it supplied?
Worked example 3 — working backwards. J of work moves a charge of C between two points. Find the potential difference.
Worked example 4 — combining the two relations. A current of A flows for s through a V source. How much energy is used?
Notice that the two formulas chain together naturally, and that chain is the whole of the energy calculation you will meet again in Part 3.
Why a potential difference is needed at all. Electrons will not drift on their own; something has to keep pushing them. A cell maintains a potential difference across the circuit, which is what keeps the charge moving — and the moment the cell is exhausted, the difference disappears and the current stops.
How potential difference is measured. A voltmeter is connected in parallel across the two points, and it must have a very high resistance so that almost no current is diverted into it.
So the two meters are connected in opposite ways for opposite reasons. The ammeter goes in series and has low resistance; the voltmeter goes in parallel and has high resistance. Each is designed not to disturb the quantity it measures, and swapping their connections is a standard examination trap.
How do you draw a circuit diagram with the standard symbols?
Use the agreed symbol for every component, join them with straight lines, and mark the direction of the current.
The symbols the syllabus expects.
- A cell — a long thin line for the positive terminal and a short thick line for the negative one
- A battery — two or more cells drawn in a row, joined end to end
- A plug key or switch — shown open or closed, drawn in the circuit line
- A wire joint — a dot where wires genuinely meet
- A resistor of fixed resistance — a plain rectangle
- A variable resistance or rheostat — a rectangle with an arrow across it
- An ammeter — a circle with the letter A, drawn in series
- A voltmeter — a circle with the letter V, drawn in parallel
- An electric bulb — a circle with a cross inside
How to lay out a diagram that earns full marks.
- Draw the circuit as a rectangle with the components on its sides, not as a tangle of curved wires
- Put the cell or battery on one side and mark the positive and negative terminals
- Show the ammeter in the main line and the voltmeter across the component whose potential difference is being measured
- Mark the direction of conventional current with an arrow, from the positive terminal outward
- Include the key, since a circuit with no switch cannot be broken
Worked example — the circuit for verifying Ohm's law. To measure the resistance of a conductor you need a circuit containing:
- A battery with a key
- A rheostat to vary the current
- An ammeter in series with the conductor, to read the current
- A voltmeter in parallel with the conductor, to read the potential difference
The rheostat is the component that makes the experiment work. Without it you could take only one reading; with it you can take several pairs of and values and see whether the ratio stays constant. An experiment that produces one reading proves nothing, which is why the variable resistance is in every version of this circuit.
The two mistakes that cost marks in a diagram question. Putting the ammeter in parallel, which would short out the conductor and give a dangerously large current, and putting the voltmeter in series, which would nearly stop the current because of its high resistance. The position of each meter is not a convention but a consequence of its resistance.
The symbols the syllabus expects.
- A cell — a long thin line for the positive terminal and a short thick line for the negative one
- A battery — two or more cells drawn in a row, joined end to end
- A plug key or switch — shown open or closed, drawn in the circuit line
- A wire joint — a dot where wires genuinely meet
- A resistor of fixed resistance — a plain rectangle
- A variable resistance or rheostat — a rectangle with an arrow across it
- An ammeter — a circle with the letter A, drawn in series
- A voltmeter — a circle with the letter V, drawn in parallel
- An electric bulb — a circle with a cross inside
How to lay out a diagram that earns full marks.
- Draw the circuit as a rectangle with the components on its sides, not as a tangle of curved wires
- Put the cell or battery on one side and mark the positive and negative terminals
- Show the ammeter in the main line and the voltmeter across the component whose potential difference is being measured
- Mark the direction of conventional current with an arrow, from the positive terminal outward
- Include the key, since a circuit with no switch cannot be broken
Worked example — the circuit for verifying Ohm's law. To measure the resistance of a conductor you need a circuit containing:
- A battery with a key
- A rheostat to vary the current
- An ammeter in series with the conductor, to read the current
- A voltmeter in parallel with the conductor, to read the potential difference
The rheostat is the component that makes the experiment work. Without it you could take only one reading; with it you can take several pairs of and values and see whether the ratio stays constant. An experiment that produces one reading proves nothing, which is why the variable resistance is in every version of this circuit.
The two mistakes that cost marks in a diagram question. Putting the ammeter in parallel, which would short out the conductor and give a dangerously large current, and putting the voltmeter in series, which would nearly stop the current because of its high resistance. The position of each meter is not a convention but a consequence of its resistance.
Formula
What does Ohm's law say, and what does the V-I graph tell you?
The current through a conductor is directly proportional to the potential difference across it, provided the temperature stays constant.
The constant is the resistance of the conductor, measured in ohms and written with the symbol for ohm. From the relation,
So one ohm is the resistance of a conductor through which a current of one ampere flows when a potential difference of one volt is applied.
Worked example 1. A potential difference of V drives a current of A through a resistor. Find its resistance.
Worked example 2. What current flows through a ohm resistor connected across a V battery?
Worked example 3. What potential difference is needed to drive A through a ohm resistor?
Now the graph. Take several readings of and for the same conductor, using the rheostat to change the current. A typical set:
- V with A
- V with A
- V with A
**Compute for each**: , , — **constant at ohms, which is exactly what Ohm's law claims.
Plotted, those points lie on a straight line through the origin, and the slope tells you the resistance:
- If is on the vertical axis**, the slope is , which is ** itself
- If is on the vertical axis**, the slope is , which is **
So always check which quantity is on which axis before reading a slope. Both graphs are straight lines through the origin, and both are correct — but the number you read off means different things.
Why the line passes through the origin.** No potential difference means no current, so the point must be on the graph. A straight line that misses the origin is not obeying Ohm's law, and that is one way a question tests the law rather than the arithmetic.
The condition that is part of the law. Ohm's law holds only if the temperature is constant. A filament lamp heats up as the current rises, its resistance increases, and its V-I graph curves instead of staying straight. A curved V-I graph does not mean the measurement was wrong — it means the conductor is not obeying Ohm's law under those conditions, and the filament lamp is the standard example.
The constant is the resistance of the conductor, measured in ohms and written with the symbol for ohm. From the relation,
So one ohm is the resistance of a conductor through which a current of one ampere flows when a potential difference of one volt is applied.
Worked example 1. A potential difference of V drives a current of A through a resistor. Find its resistance.
Worked example 2. What current flows through a ohm resistor connected across a V battery?
Worked example 3. What potential difference is needed to drive A through a ohm resistor?
Now the graph. Take several readings of and for the same conductor, using the rheostat to change the current. A typical set:
- V with A
- V with A
- V with A
**Compute for each**: , , — **constant at ohms, which is exactly what Ohm's law claims.
Plotted, those points lie on a straight line through the origin, and the slope tells you the resistance:
- If is on the vertical axis**, the slope is , which is ** itself
- If is on the vertical axis**, the slope is , which is **
So always check which quantity is on which axis before reading a slope. Both graphs are straight lines through the origin, and both are correct — but the number you read off means different things.
Why the line passes through the origin.** No potential difference means no current, so the point must be on the graph. A straight line that misses the origin is not obeying Ohm's law, and that is one way a question tests the law rather than the arithmetic.
The condition that is part of the law. Ohm's law holds only if the temperature is constant. A filament lamp heats up as the current rises, its resistance increases, and its V-I graph curves instead of staying straight. A curved V-I graph does not mean the measurement was wrong — it means the conductor is not obeying Ohm's law under those conditions, and the filament lamp is the standard example.
Exam tip
What layout keeps an electricity numerical safe?
Write the given quantities with their units, convert everything to SI, then the formula, then the substitution. Most lost marks here are unit conversions, not physics.
- Convert minutes to seconds before using . Four minutes is s
- Write the unit on every line, and give the answer with its unit — a number alone is incomplete
- State the formula before substituting: **, then the numbers
- **Use C for the charge on an electron when counting electrons
- Say which direction you mean: conventional current from positive to negative, electron drift the opposite way
- Place the ammeter in series and the voltmeter in parallel, and give the reason — low resistance and high resistance respectively
- Check which axis carries before reading a slope from a graph
- State the constant-temperature condition whenever you quote Ohm's law
The misconception to name. A cell does not store charge and pump it out; it maintains a potential difference. The charge was already in the circuit. A V cell means every coulomb gains joules** as it passes through, and that energy interpretation is what the definition is telling you — which is why the volt is a joule per coulomb and not a quantity of electricity.
- Convert minutes to seconds before using . Four minutes is s
- Write the unit on every line, and give the answer with its unit — a number alone is incomplete
- State the formula before substituting: **, then the numbers
- **Use C for the charge on an electron when counting electrons
- Say which direction you mean: conventional current from positive to negative, electron drift the opposite way
- Place the ammeter in series and the voltmeter in parallel, and give the reason — low resistance and high resistance respectively
- Check which axis carries before reading a slope from a graph
- State the constant-temperature condition whenever you quote Ohm's law
The misconception to name. A cell does not store charge and pump it out; it maintains a potential difference. The charge was already in the circuit. A V cell means every coulomb gains joules** as it passes through, and that energy interpretation is what the definition is telling you — which is why the volt is a joule per coulomb and not a quantity of electricity.
Did you know
Why does a bulb light the instant you press the switch?
The electrons in a copper wire drift astonishingly slowly — far slower than a person walks. Yet a bulb at the far end of a long wire lights the moment the switch closes. Those two facts sound contradictory and are not.
The wire is already full of electrons before you do anything. Closing the switch does not send electrons on a journey from the switch to the bulb; it sets all the electrons in the circuit drifting at once, including the ones already inside the filament. The bulb lights because its own electrons start moving, not because any electron has arrived from elsewhere.
The pipe comparison is exact. Turn a tap and water comes out immediately, even though the water reaching you was already in the pipe near the tap. What travels quickly is the push, not the material. In a circuit the push is the electric field, which is established almost instantly along the whole wire.
Three consequences you can check.
- A longer wire does not make a bulb light noticeably later, because the field is established along it almost at once
- A break anywhere in the circuit stops the current everywhere, instantly — which is why one blown fuse darkens a whole line
- The current is the same at every point in a simple series circuit, because the electrons are not piling up anywhere
That last point is worth stating carefully, because it undoes a common belief. The current is not used up as it goes round. The same number of coulombs per second passes through the bulb as leaves the cell, and what is used up is the energy each coulomb was carrying — which is why the potential difference falls across the bulb while the current does not.
And that is the difference between the two quantities in one sentence. Current is conserved round a simple circuit; energy per coulomb is spent. Confusing them produces the idea that a bulb consumes current, and the definitions in this chapter exist precisely to keep them apart.
The wire is already full of electrons before you do anything. Closing the switch does not send electrons on a journey from the switch to the bulb; it sets all the electrons in the circuit drifting at once, including the ones already inside the filament. The bulb lights because its own electrons start moving, not because any electron has arrived from elsewhere.
The pipe comparison is exact. Turn a tap and water comes out immediately, even though the water reaching you was already in the pipe near the tap. What travels quickly is the push, not the material. In a circuit the push is the electric field, which is established almost instantly along the whole wire.
Three consequences you can check.
- A longer wire does not make a bulb light noticeably later, because the field is established along it almost at once
- A break anywhere in the circuit stops the current everywhere, instantly — which is why one blown fuse darkens a whole line
- The current is the same at every point in a simple series circuit, because the electrons are not piling up anywhere
That last point is worth stating carefully, because it undoes a common belief. The current is not used up as it goes round. The same number of coulombs per second passes through the bulb as leaves the cell, and what is used up is the energy each coulomb was carrying — which is why the potential difference falls across the bulb while the current does not.
And that is the difference between the two quantities in one sentence. Current is conserved round a simple circuit; energy per coulomb is spent. Confusing them produces the idea that a bulb consumes current, and the definitions in this chapter exist precisely to keep them apart.
Exam relevance
How is Ohm's law examined in JEE and NEET?
This is foundation work for Class 12 Current Electricity, one of the most heavily examined chapters in both JEE Main and NEET.
Where it leads. Class 12 keeps unchanged and adds drift velocity, which explains microscopically why the law holds, together with the relation between current and the number density of electrons. The electron-counting calculation you do here is the first step of that derivation, and the formula of Class 12 is its completed form.
Where potential difference leads. The definition becomes electric potential in Class 12 Electrostatic Potential and Capacitance, where it is defined as the work done per unit charge in bringing a charge from infinity. The joule-per-coulomb reading of the volt is the same there, and questions on energy stored in a capacitor use it directly.
Where the meters lead. The reasons an ammeter has low resistance and a voltmeter high resistance become quantitative in Class 12, where a galvanometer is converted into either by adding a shunt or a series resistance, and the required value is calculated. JEE Main sets those numericals, and they assume exactly the reasoning in this chapter.
Where the V-I graph leads. Non-ohmic conductors — the filament lamp, the diode, the thermistor — are compared by their V-I graphs in Class 12, and identifying a device from its graph is a standard question. The curved graph of a filament lamp is the first example of it.
Question types to expect. At this level: numericals on , and , circuit diagrams, and slope reading. In competitive papers: drift-velocity numericals, meter-conversion problems, and assertion-reason items on why current is the same throughout a series circuit.
The single trap that costs marks. Reading a slope without checking the axes. **If is plotted on the vertical axis the slope is , not — and a paper that draws the graph the less familiar way is testing exactly that. Always label the axes in your own working before reading anything off.
A second trap. Forgetting that Ohm's law needs constant temperature. A question mentioning a filament lamp or a heated wire is telling you the law will not hold**, and an answer that applies regardless has missed the point of the question.
Board versus competitive emphasis. The CBSE paper marks the formula, the substitution, the unit and the labelled diagram; a competitive paper marks a number or an identification. The transferable habit is writing the units on every line — in Class 12 the same discipline catches errors in problems with far more steps.
Where it leads. Class 12 keeps unchanged and adds drift velocity, which explains microscopically why the law holds, together with the relation between current and the number density of electrons. The electron-counting calculation you do here is the first step of that derivation, and the formula of Class 12 is its completed form.
Where potential difference leads. The definition becomes electric potential in Class 12 Electrostatic Potential and Capacitance, where it is defined as the work done per unit charge in bringing a charge from infinity. The joule-per-coulomb reading of the volt is the same there, and questions on energy stored in a capacitor use it directly.
Where the meters lead. The reasons an ammeter has low resistance and a voltmeter high resistance become quantitative in Class 12, where a galvanometer is converted into either by adding a shunt or a series resistance, and the required value is calculated. JEE Main sets those numericals, and they assume exactly the reasoning in this chapter.
Where the V-I graph leads. Non-ohmic conductors — the filament lamp, the diode, the thermistor — are compared by their V-I graphs in Class 12, and identifying a device from its graph is a standard question. The curved graph of a filament lamp is the first example of it.
Question types to expect. At this level: numericals on , and , circuit diagrams, and slope reading. In competitive papers: drift-velocity numericals, meter-conversion problems, and assertion-reason items on why current is the same throughout a series circuit.
The single trap that costs marks. Reading a slope without checking the axes. **If is plotted on the vertical axis the slope is , not — and a paper that draws the graph the less familiar way is testing exactly that. Always label the axes in your own working before reading anything off.
A second trap. Forgetting that Ohm's law needs constant temperature. A question mentioning a filament lamp or a heated wire is telling you the law will not hold**, and an answer that applies regardless has missed the point of the question.
Board versus competitive emphasis. The CBSE paper marks the formula, the substitution, the unit and the labelled diagram; a competitive paper marks a number or an identification. The transferable habit is writing the units on every line — in Class 12 the same discipline catches errors in problems with far more steps.
Key takeaways
What should you know before resistance and resistivity?
Three quantities, three formulas and one condition.
- Current is charge per unit time: , with A C/s
- Convert time to seconds before using it; four minutes is s
- **One coulomb is about electrons**, since each carries C
- Conventional current flows from positive to negative; electrons drift the opposite way
- Potential difference is work per unit charge: , with V J/C — so a V cell gives every coulomb joules
- An ammeter goes in series and has low resistance; a voltmeter goes in parallel and has high resistance
- Ohm's law: , valid at constant temperature; resistance , and one ohm is one volt per ampere
- The V-I graph is a straight line through the origin. With on the vertical axis the slope is ; with on the vertical axis it is
- A filament lamp gives a curved graph, because it heats up and is not ohmic
- Current is the same throughout a series circuit — what is used up is the energy per coulomb, not the current
The sharpest self-test is the chained numerical. Take a V source driving A for s, find the charge and then the energy, and check that you converted nothing wrongly along the way.
- Current is charge per unit time: , with A C/s
- Convert time to seconds before using it; four minutes is s
- **One coulomb is about electrons**, since each carries C
- Conventional current flows from positive to negative; electrons drift the opposite way
- Potential difference is work per unit charge: , with V J/C — so a V cell gives every coulomb joules
- An ammeter goes in series and has low resistance; a voltmeter goes in parallel and has high resistance
- Ohm's law: , valid at constant temperature; resistance , and one ohm is one volt per ampere
- The V-I graph is a straight line through the origin. With on the vertical axis the slope is ; with on the vertical axis it is
- A filament lamp gives a curved graph, because it heats up and is not ohmic
- Current is the same throughout a series circuit — what is used up is the energy per coulomb, not the current
The sharpest self-test is the chained numerical. Take a V source driving A for s, find the charge and then the energy, and check that you converted nothing wrongly along the way.