First slide

Electrical power

Question

Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in the two cases is

Easy

A

2:1
B

1: 2
C

4 : 1
D

1 : 4

Solution

In series, the equivalent resistance = 2 R
In parallel, the equivalent resistance = $(\frac{R}{2})$
Power in series $P_{s} = \frac{V^{2}}{2 R}$
Power in parallel $P_{p} = \frac{V^{2}}{(\frac{R}{2})} = \frac{2 V^{2}}{R}$
$∴$ $\frac{P_{S}}{P_{p}} = \frac{1}{4}$

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