Question

two conducting wires of same material and of equal length and equal diameter are first connected in series and then in parallel in an electric circuit what is the ratio of the heat in series and parallel combination​

Answer 1

Explanation:

$\sf \: R = \frac{ ρl}{A} \\ \\ \\ \sf \:picture \: \: 1. \: \: i \: = \frac{v}{2R } \\ \\ \\ \sf \: picture \: \: 2. \: \: req = \frac{product }{sum} \\ \\ \\ \sf \implies \: \frac{R^2}{2R} = \frac{R}{2} \\ \\ \\ \sf \: i \: = \frac{v}{R} = \frac{v}{ \frac{R}{2} } = \frac{2v}{2} \\ \\ \\ \sf \: H = pxt </p><p> \\ \\ \\ \sf \: </p><p>P_i = i^2 \: Req = \frac{ {v}^{2} }{ {4R}^{2} } = \frac{ {v}^{2} }{ { \cancel{4R}}^{ \cancel{2} }} \times \cancel{2R} = \frac{ {v}^{2} }{2R} \\ \\ \\ \sf \: P_2 = {i}^{2} \: Req = \frac{ \cancel{4} {v}^{2} }{ {R}^{2} } \times \frac{R}{2} = \frac{ {2v}^{2} }{R} \\ \\ \\ \sf \: \frac{H_1 }{H_2} = \frac{p_1 \times \cancel{t}}{p_2 \times \cancel{t}} = \frac{p_1}{p_2} = \frac{ \cancel{{v}^{2}} }{2 \cancel{R} } \times \frac{ \cancel{R}}{2 { \cancel{v}}^{2} } = \frac{1}{4}$