Two conducting wires of the same material and of equal length and equal diameter are first connected in parallel and then in series in a circuit across the same potential difference. What will be the ratio of heat produced in parallel and series combinations?

Let the resistance of each wire be R. In parallel combination, the equivalent resistance R_p = R/2. In series combination, R_s = 2R. The heat produced H = V²t/R when same potential difference V is applied for time t. For parallel: H_p = V²t/(R/2) = 2V²t/R. For series: H_s = V²t/(2R). The ratio H_p : H_s = (2V²t/R) : (V²t/2R) = 2 : (1/2) = 4 : 1. Therefore, the heat produced in parallel is 4 times that in series, giving the ratio 4:1.