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  • Which of the four resistances P, Q, R and S generate the greatest amount of heat when a  current flows from A to B? <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUoAAACKCA

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

Option: 1

Q


Option: 2

S


Option: 3

P


Option: 4

R


Answers (1)

best_answer

Let net resistance of the upper branch and lower branch as R_1 \ \ and \ \ R_2 Respectively

\begin{aligned} &R_{1}=P+Q=2 \Omega+4 \Omega=6 \Omega\\ &R_{2}=R+S=1 \Omega+2 \Omega=3 \Omega \end{aligned}

Let current through the upper branch and lower branch as I_1 \ \ and \ \ I_2 Respectively

\begin{aligned} &I_{1} R_{1}=I_{2} R_{2}\\ & \Rightarrow I_{1}=\frac{R_{2}}{R_{1}} I_{2}=\frac{3}{6} I_{2}=\frac{I_{2}}{2} \end{aligned}

\text { Heat flow } =\mathrm{H}=\mathrm{I}^{2} \mathrm{Rt}

\begin{aligned} &\text { For } Q, H_{Q}=I_{1}^{2} R_Q t=\frac{I_{2}^{2}}{4} \times 4 t=I_{2}^{2} t\\ &\text { For } S, H_{S}=I_{2}^{2}R_ S t=I_{2}^{2} \cdot 2 t=2 I_{2}^{2} t \end{aligned}

\thereforeGreatest amount of heat generated by S.

Posted by

avinash.dongre

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