Current, Potential Difference and E.M.F.

Three quantities that describe electricity, defined by three equations. As one tutor put it: don’t memorise the definitions — memorise the formula and read the definition off it.

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1. Charge and current

Charge (Q) is measured in coulombs (C).

Current is the RATE OF FLOW of charge. I = Q / t, so Q = I t

Current is measured in amperes (amps, A). One amp is one coulomb per second.

“The flow of charge” is not a complete definition — current is the RATE of flow of charge, i.e. charge per unit time. Defining it as just “the flow of charge” was a recorded error, and it loses the mark.

Read the definition off the formula. I = Q/t says “charge divided by time”, which is charge per second — the rate of flow. This is the technique tutors recommended, and it works for all three quantities on this page.

Example: a current of 3 A flows for 2 minutes. How much charge passes?

• t = 2 × 60 = 120 s
• Q = I t = 3 × 120 = 360 C

Convert time to SECONDS. Forgetting this was a recorded error and is the most common slip in Q = It.

In metals, the moving charges are free electrons. In electrolytes, they are ions.

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2. Conventional current and electron flow

Conventional current flows from positive to negative around the external circuit. Electrons actually flow from negative to positive — the opposite direction.

The convention was fixed before the electron was discovered, and it has been kept ever since.

Both directions are “correct” — they just describe different things. Confusion between the two was recorded twice. If a question asks about current, use positive → negative; if it asks about electron flow, use negative → positive.

Drift speed: individual electrons drift very slowly (fractions of a mm per second), but the electric field is established almost instantly throughout the circuit, so a lamp lights the moment you close the switch.

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3. Potential difference

Potential difference (p.d., voltage) is the work done (energy transferred) per unit charge between two points.

V = W / Q, so W = V Q

Measured in volts (V). One volt is one joule per coulomb.

What it means physically: p.d. across a component is the energy given up by each coulomb of charge as it passes through that component.

Measured with a voltmeter, connected in PARALLEL across the component.

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4. Electromotive force (e.m.f.)

E.m.f. is the energy supplied to each unit of charge by a source (a cell, battery or generator).

Also measured in volts.

The distinction:

E.m.f. — energy given TO the charge by the source. P.d. — energy given UP by the charge in a component.

E.m.f. is not “the force of a battery”. Defining it incorrectly was a recorded error — despite its name, e.m.f. is not a force at all; it is an energy per unit charge, measured in volts.

Cells in series:

The total e.m.f. is the SUM of the individual e.m.f.s — provided they are connected the same way round.

Three 1.5 V cells in series give 4.5 V.

To find one cell’s e.m.f. from the total, DIVIDE by the number of cells — but only when they are identical and in series. A recorded error divided a total voltage by the number of cells in a situation where that wasn’t valid; check the arrangement first.

Cells in parallel (identical cells) give the same e.m.f. as one cell, but can supply current for longer.

Connect cells the same way round. Reversing one subtracts its e.m.f. from the total.

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5. The three equations together

Quantity	Equation	Unit
Current	I = Q/t	A
Potential difference	V = W/Q	V
Resistance	V = IR	Ω
Power	P = VI	W
Energy	E = VIt	J

Example: 240 C of charge transfers 2880 J of energy through a lamp.

• V = W/Q = 2880 ÷ 240 = 12 V

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6. a.c. and d.c.

d.c. (direct current) — flows in one direction only; from cells and batteries. a.c. (alternating current) — reverses direction regularly; from the mains and generators.

Confusing a.c. with d.c. in circuits was a recorded error. Cells give d.c.; the mains gives a.c.

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7. Circuit behaviour

• Closing a switch completes the circuit, allowing current to flow
• Adding resistance in series reduces the current everywhere in that loop
• A break anywhere in a series circuit stops all current

A switch changes the circuit’s total resistance from effectively infinite (open) to a normal value (closed). Misunderstanding how a switch affects resistance and current was a recorded error.

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8. Mistakes that cost marks

Defining current as “the flow of charge” without rate.

Not converting time to seconds in Q = It.

Confusing conventional current with electron flow.

Calling e.m.f. a force.

Confusing e.m.f. with potential difference.

Dividing a total voltage by the number of cells when it isn’t valid.

Adding e.m.f.s of cells connected in opposition.

Confusing a.c. with d.c.

Putting the voltmeter in series.

Omitting units — A, C, V, J.

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Frequently asked questions

What is current? The rate of flow of charge: I = Q/t, in amperes.

What is the unit of charge? The coulomb (C).

How do I calculate charge? Q = I t, with time in seconds.

Which way does current flow? Conventional current flows positive to negative; electrons flow the other way.

What is potential difference? The energy transferred per unit charge: V = W/Q, in volts.

What is e.m.f.? The energy supplied per unit charge by a source — also in volts.

Is e.m.f. a force? No — despite the name, it is an energy per unit charge.

What is the total e.m.f. of cells in series? The sum of the individual e.m.f.s, if connected the same way round.

What is the difference between a.c. and d.c.? a.c. reverses direction; d.c. flows one way only.

Where does a voltmeter go? In parallel across the component.

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Quick revision checklist

• I can define current as the rate of flow of charge
• I know Q = It and convert time to seconds
• I know the unit of charge is the coulomb
• I know conventional current and electron flow directions
• I can define potential difference as energy per unit charge
• I can define e.m.f. and distinguish it from p.d.
• I know e.m.f. is not a force
• I can combine cells in series and in parallel
• I know what happens if a cell is reversed
• I can use V = W/Q and P = VI
• I can distinguish a.c. from d.c.
• I know how a switch affects resistance and current
• I can derive definitions from the formulae
• I give units on every answer

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These notes cover current, potential difference and e.m.f. in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.