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  • Consider a wire loop as shown in the figure. If the resistance per unit length is , find the resistance between P & Q i.e. <img alt="R_{PQ}" s

Consider a wire loop as shown in the figure. If the resistance per unit length is \lambda, find the resistance between P & Q i.e. R_{PQ} is

 

Option: 1

\left(\frac{\frac{\pi^2}{8}+\frac{\pi}{2}}{1+\pi / 2}\right) 2 a \lambda


Option: 2

\left(\frac{\frac{\pi^2}{8}+\frac{\pi}{2}}{2+\pi}\right) a \lambda


Option: 3

\left(\frac{\frac{\pi^2}{8}+\frac{\pi}{2}}{2+\pi}\right) a \lambda


Option: 4

None of the above


Answers (1)

best_answer

In the given figure, the equivalent circuit can be redrawn as

From symmetry, OP & Q are at the same potential and hence the circuit can be replaced by

The only change is the separation of O into O & O{}'. The resistance in one of the
arms is

\mathrm{R}_{\mathrm{PCOAQ}}=2 \frac{\pi}{4} \xi+\frac{2 \cdot \frac{\pi}{2} \xi}{2+\frac{\pi}{2}}

\therefore \text { The resistance } \mathrm{RPQ}_P=\frac{1}{2} \mathrm{R}_{\mathrm{PCOAQ}}=\left(\frac{\pi}{4} \xi+\frac{\pi / 2 \xi}{2+\pi / 2}\right)

\begin{aligned} & =\left(\frac{\frac{\pi^2}{8}+\frac{\pi}{2}}{2+\pi / 2}\right) \\ & {[\because \xi=a \lambda]} \end{aligned}

 

 

Posted by

HARSH KANKARIA

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