The diagram shows a d.c. circuit. What is the resistance between the points P and Q due to the resistance network?

Question 10

The diagram shows a d.c. circuit.

What is the resistance between the points P and Q due to the resistance network?

A 0.47 Ω          B 2.1 Ω           C 3.0 Ω           D 21 Ω

Reference: Past Exam Paper – June 2011 Paper 12 Q38

Solution:

Answer: C.

We need to simplify the resistances.

Consider the two 6 Ω resistors in parallel. Let their combined resistance be R₁.

1 / R₁ = 1/6 + 1/6

R₁ = [1/6 + 1/6]^-1 = 3 Ω

This 3 Ω combined resistance is in series with the 3 Ω resistor in the lower branch.

Combined resistance in the lower branch = 3 + 3 = 6 Ω

Equivalent resistance between the points P and Q,

R_T = [1/6 + 1/(3+3)]^-1 = 3 Ω