Physics · Electricity

Relating current, charge and time

You know the formula, but your answer is out by a factor of sixty.

Current is the rate of flow of charge. The relationship I = Q/t links current in amperes, charge in coulombs and time in seconds.

This lesson is part of SPM Physics electricity. The next lesson is applying potential difference, resistance and Ohm’s law.

How do I use I = Q/t?

List the quantities with their units first. Convert anything that is not in amperes, coulombs or seconds, then rearrange.

Want	Formula	Unit
Current	I = Q ÷ t	A
Charge	Q = I × t	C
Time	t = Q ÷ I	s

Worked example: from current to electrons

A current of 3.0 A flows through a heater element for 40 s. Find the charge, then the number of electrons that pass a point in the element.

Charge: Q = I × t = 3.0 × 40 = 120 C.
Electrons: N = Q ÷ e = 120 ÷ (1.6 × 10⁻¹⁹) = 7.5 × 10²⁰.

The second step reuses the charge from the first. Write the unit with each answer: C for charge, and no unit for the number of electrons.

The mistake that loses marks

A current of 0.50 A flows for 2 minutes, and a student writes Q = 0.50 × 2 = 1.0 C. The time was left in minutes.

Convert first: 2 minutes = 120 s, so Q = 0.50 × 120 = 60 C. The wrong answer is 60 times too small, and a units line at the top would have caught it.

Check yourself

A charge of 450 C flows through a lamp in 5.0 minutes. Find the current, and state which unit conversion you made.

Answer

Convert 5.0 minutes to seconds: 5.0 × 60 = 300 s.

I = Q ÷ t = 450 ÷ 300 = 1.5 A.

Check the size: 1.5 coulombs each second over 300 seconds gives 450 coulombs.

What to study next

Current alone does not say how much energy a component transfers. Applying potential difference, resistance and Ohm’s law adds the second quantity, and the units and significant figure checker can check your working.

Test the topic with the electricity practice set. For a teacher to go through your unit conversions with you, see online one-to-one Physics tuition or the one-hour trial class (from RM50).

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Common questions

What does one ampere mean?

One ampere is a flow of one coulomb of charge each second. So 1 A = 1 C s⁻¹. A current of 3 A means 3 coulombs pass a point every second. The formula I = Q/t is just this meaning written as an equation.

Do I convert minutes to seconds every time?

Yes. The ampere is defined with seconds, so time must be in seconds when you use I = Q/t. Two minutes is 120 s. Milliamperes also need converting: 250 mA is 0.250 A.

What is the charge of one electron?

The charge of one electron is 1.6 × 10⁻¹⁹ C, which you use to count electrons from a total charge. The number of electrons equals the total charge divided by this value.

Is current used up in a circuit?

No. In a series circuit the same current leaves a component as enters it. Energy is transferred, but charge is not used up. Some students think a lamp uses up current, but an ammeter on each side of the lamp shows the same reading.

Keep going

In one-to-one Physics lessons a teacher can watch your unit conversions line by line. That is where current and charge answers usually go wrong, and where self-marking rarely looks.

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