NDA 1 2025 GAT, question 128

Topic: Physics

Q128

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

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

Solution.

Answer: (b) 4 : 1

Each wire has the same resistance $R$ .
The parallel combination has resistance $R/2$ and the series combination has resistance $2R$ .
For the same voltage and time, $H = V^{2}t/R_{eq}$ .
Hence $H_{parallel}/H_{series} = (2R)/(R/2) = 4$ .
The ratio is $4:1$ .