In the circuit shown here, what is the value | vedclass

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(C) The circuit consists of a $3 \, \Omega$ resistor in series with a parallel combination of a $10 \, \Omega$ resistor and a branch containing a $3 \

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$\sqrt{69} \, \Omega$

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(C) The circuit consists of a $3 \, \Omega$ resistor in series with a parallel combination of a $10 \, \Omega$ resistor and a branch containing a $3 \, \Omega$ resistor in series with $R$.The equivalent resistance $R_{eq}$ between $P$ and $Q$ is given by:$R_{eq} = 3 + \frac{10 	imes (3 + R)}{10 + (3 + R)}$Given that $R_{eq} = R$, we substitute $R$ for $R_{eq}$:$R = 3 + \frac{10(3 + R)}{13 + R}$$R - 3 = \frac{30 + 10R}{13 + R}$$(R - 3)(13 + R) = 30 + 10R$$13R + R^2 - 39 - 3R = 30 + 10R$$R^2 + 10R - 39 = 30 + 10R$$R^2 = 69$$R = \sqrt{69} \, \Omega$.

In the circuit shown here, what is the value of the unknown resistor $R$ so that the total resistance of the circuit between points $P$ and $Q$ is also equal to $R$?

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