The equivalent resistance between the points | vedclass

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(C) Let the nodes be labeled. The circuit consists of five $1\,\Omega$ resistors. By analyzing the circuit,we see that the middle three resistors are

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$2\frac{1}{3}$

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(C) Let the nodes be labeled. The circuit consists of five $1\,\Omega$ resistors. By analyzing the circuit,we see that the middle three resistors are connected in parallel. Let the resistance of these three parallel resistors be $R_p$. Since each is $1\,\Omega$,we have $\frac{1}{R_p} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1} = 3$,so $R_p = \frac{1}{3}\,\Omega$. This parallel combination is in series with the two $1\,\Omega$ resistors at the ends. Therefore,the total equivalent resistance $R_{AB} = 1 + \frac{1}{3} + 1 = 2 + \frac{1}{3} = 2\frac{1}{3}\,\Omega$.

The equivalent resistance between the points $A$ and $B$ is (in $\Omega$):

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