Ohm's law and power practice

Given two of the quantities, find the third. Type your answer and it is marked on the spot, with the working shown if you miss. An answer within 1% counts, and the unit is optional — 2.5 and 2.5 A are both fine. Stuck? Hint shows the formula and nothing else. Start on Basic if this is new; Field uses the supply voltages you will actually meet; Power drills the squared forms.

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Cet exercice a besoin de JavaScript pour générer et corriger les questions. Activez-le pour vous exercer — l’explication ci-dessous fonctionne dans les deux cas.

The wheel: every rearrangement in one drawing

Two laws are all there is. Ohm's law, V = I × R, and the power law, P = V × I. Everything on the wheel is one of those two rearranged, or the two combined. Find the quantity you want at the hub, then read outward: the three formulas in that quadrant are the three pairs of things you might already know.

V = I × Rvolts = amps × ohms. Cover the one you want; what is left is the formula.
P = V × Iwatts = volts × amps. Swap in I × R for V and you get P = I² × R.

Three worked examples, one per rearrangement

Each one is written out the way I would do it on the back of a box: name what you know, pick the formula off the wheel, then arithmetic. The numbers are practice numbers — they are not ratings for anything.

1. Find the current — a 120 V supply, a 24 Ω heater element

Known: V = 120 V, R = 24 Ω. Wanted: I.
On the wheel, I from V and R is I = V ÷ R.
I = 120 ÷ 24 = 5 A.

Check it the other way

Put the answer back: V = I × R = 5 × 24 = 120 V. Same supply, so the current is right. Get in the habit — a reversed check catches a slipped decimal every time.

2. Find the resistance — a load on 240 V draws 2.5 A

Known: V = 240 V, I = 2.5 A. Wanted: R.
On the wheel, R from V and I is R = V ÷ I.
R = 240 ÷ 2.5. Two-and-a-half goes into 240 ninety-six times: 96 Ω.

Doing 240 ÷ 2.5 without a calculator

Double both: 480 ÷ 5 = 96. Dividing by 2.5 is the same as dividing by 5 and doubling, which is quicker than it sounds once you have done it twice.

3. Find the power — 8 A through a 15 Ω element

Known: I = 8 A, R = 15 Ω. Wanted: P. No voltage given.
On the wheel, P from I and R is P = I² × R. (P = V × I would need a V you do not have — or you could find V first: V = 8 × 15 = 120 V, then P = 120 × 8.)
Square the current first: 8² = 64. Then 64 × 15 = 960 W.

Why the current is squared

P = V × I, and V = I × R. Swap the second into the first: P = (I × R) × I = I × I × R = I² × R. The square is not a new law, it is the old two written together. The most common slip on this form is multiplying I × R and forgetting to multiply by I again — 8 × 15 = 120 is the volts, not the watts.

Try one before the drill: a 48 Ω load on 120 V — what current, and what power?

I = V ÷ R = 120 ÷ 48 = 2.5 A. Then P = V × I = 120 × 2.5 = 300 W. Or straight from the wheel: P = V² ÷ R = 14,400 ÷ 48 = 300 W. Both roads reach the same number, which is the point of a wheel.

Questions fréquentes

What is Ohm's law?

Voltage equals current times resistance: V = I × R. Rearranged, I = V ÷ R and R = V ÷ I. It ties the three basic quantities of a circuit together, so knowing any two gives you the third.

Where does power come in?

Power is voltage times current: P = V × I. Combine it with Ohm's law and you also get P = I² × R and P = V² ÷ R. The Basic and Field levels stick to the two core forms so the relationships stay clear; the Power level drills the squared forms and their inverses.

Do I need to memorise the wheel?

Not really — if you hold V = I × R and P = V × I, everything else is algebra on those two. The wheel is just every rearrangement drawn in a circle. Drill the two core laws and the rest falls out. Use the Hint button when you blank: it shows the formula and nothing else.

How exact does my answer have to be?

Within 1% of the answer counts, and the unit is optional — 2.5, 2.5 A and 2,5A all mark the same. The drill is checking that you picked the right rearrangement and did the arithmetic, not your rounding habits.

Voir aussi

Series / parallel practice — the next step: two or three resistors, and the drop across each.
Series vs parallel lighting — where the voltage sharing shows up in a circuit.
Formula sheet: Ohm's law and power wheel — the same wheel, printable.
Ohm's law worksheet — twelve on paper, with a worked answer key.
All drills

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