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Q.

Two conducting wires of the same material which are of equal length, diameter are first connected in series and then parallel in a circuit, across the same potential difference. The heat produced in series and parallel combination would be in the ratio

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a

1 : 2

b

2 : 1

c

1 : 4

d

4 : 1

answer is C.

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Detailed Solution

Two conducting wires of the same material which are of equal length, diameter are first connected in series and then parallel in a circuit, across the same potential difference. The heat produced in series and parallel combination would be in the ratio 1:4.
Given that, two wires are identical. So, their resistances will be the same. The Equivalent Resistance in series will be

2 R

and in parallel

\frac{R}{2}

.
Heat produced =

\frac{V^{2} t}{R}

For series, heat will be

\frac{V^{2} t}{2 R}

and for parallel, heat will be

\frac{{2 V}^{2} t}{R}

The ratio of heat produced will be

\frac{Hs}{Hp} = \frac{\frac{V^{2} t}{2 R}}{\frac{{2 V}^{2} t}{R}} = 1 : 4

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