wo conducting wires of the same material and

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Solution

Q.
Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then in parallel in a circuit across the same potential difference. The ratio of power produced in series and parallel combinations would be:

1 1 : 2

2 2 : 1

3 1 : 4

4 4 : 1

Ans.
(3)

As the two conducting wires are of the same material, equal lengths and equal diameters. They will have the same resistance.

Let the resistance of each wire be R and applied potential difference, V

$R_{s e r i e s} = R_{1} + R_{2} = R + R = 2 R P_{s e r i e s} = \frac{V^{2}}{R_{s e r i e s}} = \frac{V^{2}}{(2 R)} (i)$

$\frac{1}{R_{p a r a l l e l}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} = \frac{1}{R} + \frac{1}{R} R_{p a r a l l e l} = \frac{R}{2} P_{p a r a l l e l} = \frac{R}{2} P_{p a r a l l e l} = \frac{V^{2}}{R_{p a r a l l e l}} = \frac{2 V^{2}}{R} D i v i d i n g e q u a t i o n (i) b y e q u a t i o n (i i) \frac{P_{s e r i e s}}{P_{p a r a l l e l}} = \frac{1}{4}$

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