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(B) Heat produced in the circuit is inversely proportional to the resistance $R$ for a constant potential difference $V$,given by the formula $H = \fr

Vedclass · Accepted Answer

$1:4$

Vedclass · Answer

(B) Heat produced in the circuit is inversely proportional to the resistance $R$ for a constant potential difference $V$,given by the formula $H = \frac{V^2}{R} t$.Let $R$ be the resistance of each wire. If connected in series,the equivalent resistance is $R_S = R + R = 2R$.If connected in parallel,the equivalent resistance is $R_P = \frac{R 	imes R}{R + R} = \frac{R}{2}$.The ratio of heat produced in series $(H_S)$ to parallel $(H_P)$ is given by:$\frac{H_S}{H_P} = \frac{V^2 / R_S 	imes t}{V^2 / R_P 	imes t} = \frac{R_P}{R_S}$.Substituting the values of $R_S$ and $R_P$:$\frac{H_S}{H_P} = \frac{R/2}{2R} = \frac{1}{4}$.Thus,the ratio of heat produced is $1:4$.

Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be -

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