Which of the four resistances P, Q, R and S g | vedclass

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(B) The circuit consists of two parallel branches. The upper branch has resistances $P = 2 \, \Omega$ and $Q = 4 \, \Omega$ in series,so its total res

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$S$

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(B) The circuit consists of two parallel branches. The upper branch has resistances $P = 2 \, \Omega$ and $Q = 4 \, \Omega$ in series,so its total resistance is $R_1 = P + Q = 2 \, \Omega + 4 \, \Omega = 6 \, \Omega$.The lower branch has resistances $R = 1 \, \Omega$ and $S = 2 \, \Omega$ in series,so its total resistance is $R_2 = R + S = 1 \, \Omega + 2 \, \Omega = 3 \, \Omega$.Since the branches are in parallel,the potential difference across them is the same. Let $I_1$ be the current in the upper branch and $I_2$ be the current in the lower branch.$I_1 R_1 = I_2 R_2 \implies I_1 (6 \, \Omega) = I_2 (3 \, \Omega) \implies I_2 = 2 I_1$.The heat generated in a resistor is given by $H = I^2 R t$.For $P$: $H_P = I_1^2 P t = I_1^2 (2) t = 2 I_1^2 t$.For $Q$: $H_Q = I_1^2 Q t = I_1^2 (4) t = 4 I_1^2 t$.For $R$: $H_R = I_2^2 R t = (2 I_1)^2 (1) t = 4 I_1^2 t$.For $S$: $H_S = I_2^2 S t = (2 I_1)^2 (2) t = 8 I_1^2 t$.Comparing the heat values,$H_S = 8 I_1^2 t$ is the greatest. Therefore,the resistance $S$ generates the greatest amount of heat.

Which of the four resistances $P, Q, R$ and $S$ generate the greatest amount of heat when a current flows from $A$ to $B$?

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