Charge & Ohm's Law: Using the Equations

Explained

Two electrical equations, used carefully

Charge equals current multiplied by time, Q equals I times t. Potential difference equals current multiplied by resistance, V equals I times R.

Current appears in both, which is what lets you chain them together when a question gives you a charge and asks for a voltage, or the other way round.

Charge, current and time

Charge in coulombs, current in amperes, time in seconds.

A current of 0.5 A flowing for 2 minutes delivers 0.5 times 120, which is 60 C. Note the conversion: two minutes is 120 seconds, and forgetting to convert is the commonest error in this equation by a wide margin.

To find a current, divide the charge by the time. To find a time, divide the charge by the current, and remember the answer will be in seconds, so convert it back if the question wants minutes.

Ohm's law

Potential difference in volts, current in amperes, resistance in ohms.

A current of 0.15 A through a 20 ohm resistor gives 0.15 times 20, which is 3 V. To find a resistance, divide the voltage by the current. To find a current, divide the voltage by the resistance.

Currents are often given in milliamperes. Divide by 1000 to get amperes first, because a current left in milliamperes gives an answer a thousand times too large and it will not look obviously wrong.

Chaining them

A typical multi step question: a 12 V supply drives a current through a 40 ohm resistor for 30 seconds, and asks for the charge.

Find the current first from Ohm's law: 12 divided by 40 is 0.3 A. Then use Q equals I times t: 0.3 times 30 is 9 C.

The order is forced by what you have. You cannot find the charge without the current, so the resistance question comes first even though the question asked about charge.

Energy, if the question goes further

Energy transferred equals charge multiplied by potential difference, E equals Q times V. So having found 9 C at 12 V, the energy transferred is 108 J.

This follows from what a volt means: one joule per coulomb. Multiply the coulombs by the joules each one carries, and you have the total.

The habits that protect the marks

Write the equation before you put any numbers in it. Substitute, then rearrange, never the other way round, because a rearrangement done in your head cannot be credited if it goes wrong.

Convert every quantity to its standard unit first: seconds, amperes, volts, ohms, coulombs. Write the conversion as its own line.

Then check the size of the answer. A resistance of a few ohms with a few volts gives a current of around an ampere. A current of thousands of amperes from a torch battery means a conversion has gone astray.