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

Step-by-step solution

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 combination