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

Question

Aicharya · Accepted Answer

$ \begin{aligned} & \mathrm{R}_1=\mathrm{P}+\mathrm{Q}=2 \Omega+4 \Omega=6 \Omega \\ & \mathrm{R}_2=\mathrm{R}+\mathrm{S}=1 \Omega+2 \Omega=3 \Omega \\ & \mathrm{I}_1 \mathrm{R}_1=\mathrm{I}_2 \mathrm{R}_2 \\ & \mathrm{I}_1=\frac{\mathrm{R}_2}{\mathrm{R}_1} \mathrm{I}_2=\frac{3}{6} \mathrm{I}_2=\frac{\mathrm{I}_2}{2} \end{aligned} $ or $\mathrm{I}_2=2 \mathrm{I}_1$ Heat flow $\mathrm{H}=\mathrm{I}^2 \mathrm{Rt}$ For $\mathrm{Q}, \mathrm{H}_{\mathrm{Q}}=\mathrm{I}_1^2 \mathrm{Qt}=\frac{\mathrm{I}_2^2}{4} \times 4 \mathrm{t}=\mathrm{I}_2^2 \mathrm{t}$ For $\mathrm{S}, \mathrm{H}_{\mathrm{S}}=\mathrm{I}_2^2 \mathrm{St}=\mathrm{I}_2^2 \cdot 2 \mathrm{t}=2 \mathrm{I}_2^2 \mathrm{t}$ $\therefore$ Greatest amount of heat generated by $\mathrm{S}$.

Which of the four resistances $P, Q, R$ and $S$ generate the greatest amount of heat when a current flows…

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