In the circuit shown,what is the value of the | 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:$R_{eq} = 3 + \frac{10(R + 3)}{10 + (R + 3)}$Given that $R_{eq} = R$,we have:$R = 3 + \frac{10(R + 3)}{R + 13}$Subtract $3$ from both sides:$R - 3 = \frac{10R + 30}{R + 13}$Cross-multiply:$(R - 3)(R + 13) = 10R + 30$$R^2 + 13R - 3R - 39 = 10R + 30$$R^2 + 10R - 39 = 10R + 30$Subtract $10R$ from both sides:$R^2 - 39 = 30$$R^2 = 69$$R = \sqrt{69} \,\Omega$

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

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