9702/May Jun/11/2015/Q38

A wire RST is connected to another wire XY as shown.

Each wire is 100 cm long with a resistance per unit length of 10 Ω m^–1.
What is the total resistance between X and Y?
A 3.3 Ω
B 5.0 Ω
C 8.3 Ω
D 13.3 Ω

Solution:

Answer: C.

Resistance per unit length of wire = 10 Ω m^–1

Resistance of wire RST = 1m × 10 Ω m^–1 = 10 Ω

Since the wire XY is 100cm, the sum of XR + TY = 100 – 50 = 50cm

Sum of resistance of (XR+TY) = 0.5m × 10 Ω m^–1 = 5 Ω

Resistance of wire RT = 0.5m × 10 Ω m^–1 = 5 Ω

Hence the arrangement is effectively a 10 Ω resistor RST in parallel with a 5 Ω resistor RT, and in series with another 5 Ω resistor (XR+TY).

Effective resistance of parallel combination = [1/10 + 1/5]^-1 = 3.3 Ω

The total resistance is therefore 5 Ω + 3.3 Ω = 8.3 Ω.

Reference: PYQ - May/Jun 2015 Paper 11 Q38