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

The resistance of a conductor depends on its material, length, and diameter [1]. Let the resistance of each wire be R. When connected in series, the equivalent resistance is Rs = R + R = 2R [2]. When connected in parallel, the equivalent resistance is Rp = R/2 [2]. The heat produced (H) across a constant potential difference (V) over time (t) is given by Joule's law as H = (V^2 / R_eq) * t. Therefore, heat in series is Hs = (V^2 / 2R) * t, and heat in parallel is Hp = (V^2 / (R/2)) * t = (2V^2 / R) * t [2]. The ratio of heat produced in parallel to series is Hp: Hs = (2V^2 / R): (V^2 / 2R), which simplifies to 2: (1/2), resulting in a ratio of 4:1 [2].

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > What you have learnt > p. 192
2. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > H = I2 > p. 189