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

Q. 4.     Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be –

(a) 1:2             (b) 2:1             (c) 1:4             (d) 4:1

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If resistors are connected in parallel, the net resistance is given as

$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}$

$\Rightarrow \frac{1}{R_p}=\frac{1}{R}+\frac{1}{R}$

$\Rightarrow \frac{1}{R_p}=\frac{2}{R}$

$\Rightarrow R_p=\frac{R}{2}$

If resistors are connected in series, the net resistance is given as

$\Rightarrow R_s=R_1+R_2=R+R=2R$

Heat produced = H = $\frac{V^2}{R}t$

$\frac{H_s}{H_p}=\frac{\frac{V^2t}{2R}}{\frac{V^2t}{\frac{R}{2}}}$

$\Rightarrow \frac{H_s}{H_p}=\frac{1}{4}$

$\Rightarrow H_s:H_p=1:4$

Thus, option C is correct.

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