Two conducting wires of the same material and of equal lengths and equal diameters are first connected in parallel and then in series in a circuit across the same potential difference. The ratio of heat produced in parallel and series combinations is
B. 4 : 1
Let the resistance of each wire be R. When the wires are connected in parallel, the equivalent resistance is R_p = R 2 . When the wires are connected in series, the equivalent resistance is R_s = 2R. The heat produced in a circuit across a potential difference V in time t is given by H = V^2 R_ eq t. The heat produced in the parallel combination is H_p = V^2 R_p t = 2V^2 R t. The heat produced in the series combination is H_s = V^2 R_s t = V^2 2R t. The ratio of heat produced in parallel and series combinations is H_p H_s = 2V^2 R t V^2 2R t = 4. Thus, the required ratio is 4 : 1. Answer: 4 : 1
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