Question:
The ratio of the equivalent resistance of the network (shown in figure) between the points a and $b$ when switch is open and switch is closed is $\mathrm{x}: 8$. The value of $\mathrm{x}$ is
Solution:
$\mathrm{R}_{\text {eq open }}=\frac{3 \mathrm{R}}{2}$
$\mathrm{R}_{\text {eq closed }}=2 \times \frac{\mathrm{R} \times 2 \mathrm{R}}{3 \mathrm{R}}=\frac{4 \mathrm{R}}{3}$
$\frac{\mathrm{R}_{\mathrm{cq} \text { opcn }}}{\mathrm{R}_{\text {cq closed }}}=\frac{3 \mathrm{R}}{2} \times \frac{3}{4 \mathrm{R}}=\frac{9}{8}$
$\therefore x=9$
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