Question 263 of 380

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

A$\mathrm{Q}$B$\mathrm{S}$C$\mathrm{P}$D$\mathrm{R}$

Show answer and solution▾

Answer: (B) $\mathrm{S}$

$$\begin{aligned} & \mathrm{R}_1=\mathrm{P}+\mathrm{Q}=2 \Omega+4 \Omega=6 \Omega \\ & \mathrm{R}_2=\mathrm{R}+\mathrm{S}=1 \Omega+2 \Omega=3 \Omega \\ & \mathrm{I}_1 \mathrm{R}_1=\mathrm{I}_2 \mathrm{R}_2 \\ & \mathrm{I}_1=\frac{\mathrm{R}_2}{\mathrm{R}_1} \mathrm{I}_2=\frac{3}{6} \mathrm{I}_2=\frac{\mathrm{I}_2}{2} \end{aligned}$$
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 $\mathrm{S}$.

JEE Main Physics practice question on Current Electricity (Electric Power and Heating Effect of Current), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.