Circuits & Ohm's Law — Practice · Grade 12 Science

Chapter: Electricity, Magnetism & Circuits

What this practice covers

By the end of Circuits & Ohm's Law you should be able to:

10 questions, numeric, multiple choice and written answer, each with a worked explanation.

Vocabulary used: Ohm's law, series circuit, parallel circuit, equivalent resistance, electrical power.

Problem 1

A current of 2 A flows through a 5 Ω resistor. Find the voltage across it.
Answer and explanation

10 V

V = IR = 2 × 5 = 10 V.

Problem 2

A 24 V source drives a current of 3 A through a resistor. Find its resistance.
Answer and explanation

8 Ω

R = V ÷ I = 24 ÷ 3 = 8 Ω.

Problem 3

Three resistors of 4 Ω, 6 Ω, and 10 Ω are connected in series. Find the total resistance.
Answer and explanation

20 Ω

In series, resistances add: 4 + 6 + 10 = 20 Ω.

Problem 4

In a series circuit, the current flowing through each resistor is:
  1. the same through all of them
  2. larger in the bigger resistors
  3. smaller in the bigger resistors
  4. zero
Answer and explanation

the same through all of them

A series circuit has one single path, so the identical current flows through every component.

Problem 5

Two 12 Ω resistors are connected in parallel. Find their equivalent resistance.
Answer and explanation

6 Ω

1/R = 1/12 + 1/12 = 2/12 = 1/6, so R = 6 Ω. (For two equal resistors, the parallel total is always half of one.)

Problem 6

A light bulb rated at 60 W runs on a 120 V supply. What current does it draw?
Answer and explanation

0.5 A

Rearranging P = IV gives I = P ÷ V = 60 ÷ 120 = 0.5 A.

Problem 7

Two 6 Ω resistors are in parallel across 12 V. Find equivalent resistance and total current. Show the reasoning, not just the conclusion.
Hints

Kirchhoff's loop balance provides a check.

Answer and explanation

R_eq=3 Ω; I_total=12/3=4 A, with 2 A per branch.

Problem 8

Why is branch voltage equal in an ideal parallel connection?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Each branch spans the same two electrical nodes, so it has the same potential difference.

Problem 9

Equivalent resistance replaces a network at its terminalsEquivalent resistance replaces a network at its terminalsCombinationEquivalent relationFor 6 Ω and 3 ΩSeriesReq=R₁+R₂9 ΩParallel1/Req=1/R₁+1/R₂2 ΩSame 6 V sourceI=V/Req2/3 A versus 3 AEquivalent resistance matches terminal behavior, not every branch.
Original exact equivalent-resistance comparison for two positive ohmic resistors.
Interpret the supplied visual. Is a parallel equivalent larger or smaller than its smallest positive branch resistance?
Answer and explanation

Smaller for more than one finite positive branch in this ideal model.

An equivalent resistance gives the same voltage–total-current relation at a chosen pair of terminals as the ideal resistor network. Series resistances add; parallel conductances 1/R add. A 2 Ω equivalent for 6 Ω parallel with 3 Ω is smaller than either branch resistance because it offers more conducting paths. This does not mean either actual resistor changed its own resistance or that branch currents equal the total current.

Smaller for more than one finite positive branch in this ideal model.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 10

Two resistors 4 Ω and 12 Ω are in parallel across an ideal 12 V source. Find each current, total current, equivalent resistance and total power.
Answer and explanation

Currents are 3 A and 1 A; total 4 A. Req=12/4=3 Ω and P=12×4=48 W. Branch powers 36 W and 12 W sum consistently.

Currents are 3 A and 1 A; total 4 A.

Req=12/4=3 Ω and P=12×4=48 W.

Branch powers 36 W and 12 W sum consistently.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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