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

Asked by Vishal kumar | 1 year ago |  150

1 Answer

Solution :-

Let Rs and Rp be the equivalent resistance of the wires when connected in series and parallel, respectively. For the same potential difference V, the ratio of the heat produced in the circuit is given by

\( \frac{H_s}{H_p}=\frac{\frac{V^2}{R^s}t}{\frac{V^2}{R_p}t}=\frac{R_p}{R_s}\)

The equivalent resistance of resistors connected in series R, is R+R = 2R

The equivalent resistance of resistors connected in parallel Rp is \( \frac{1}{\frac{1+1}{R+R}}=\frac{R}{2}\)

Hence, the ratio of the heat produced in series and parallel combination would be

 \( \frac{H_p}{H_s}=\frac{\frac{R}{2}}{2R}=\frac{1}{4}\)

Hence, the ratio of the heat produced is 14

Answered by Shivani Kumari | 1 year ago

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