Saturday, May 13, 2017

The diagram shows a circuit containing three resistors in parallel. The battery has e.m.f. 12 V and negligible internal resistance.




Question 2
The diagram shows a circuit containing three resistors in parallel.

The battery has e.m.f. 12 V and negligible internal resistance. The ammeter reading is 3.2 A.
What is the resistance of X?

A 2.1 Ω           B 4.6 Ω           C 6.0 Ω           D 15 Ω





Reference: Past Exam Paper – November 2008 Paper 1 Q35





Solution:
Answer: D.
For a parallel combination, the p.d. across each branch is equal and in this case, the p.d. across each branch is equal to the e.m.f. of 12 V.

To know the resistance of X, we need to know the p.d. across it (= 12V) and the current flowing through it (unknown).
The current of 3.2A coming from the terminal of the battery splits at the junction.
Current across the 10Ω resistor = V/R = 12/10 = 1.2 A
Current through X = 3.2 – 1.2 – 1.2 = 0.8 A

From Ohm’s law, Resistance of X = V/I = 12 / 0.8 = 15 Ω

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