The equivalent resistance between the points | vedclass

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(C) The given circuit can be simplified by observing the symmetry. Let the points be labeled. The circuit consists of two loops in series. Each loop h

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$2 r$

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(C) The given circuit can be simplified by observing the symmetry. Let the points be labeled. The circuit consists of two loops in series. Each loop has two resistors of resistance $r$ in series, which are in parallel with another branch of two resistors of resistance $r$ in series. For the first part (left side), the two branches are in parallel, each having a resistance of $r + r = 2r$. The equivalent resistance of this part is $R_1 = \frac{2r 	imes 2r}{2r + 2r} = \frac{4r^2}{4r} = r$. Similarly, for the second part (right side), the two branches are in parallel, each having a resistance of $r + r = 2r$. The equivalent resistance of this part is $R_2 = \frac{2r 	imes 2r}{2r + 2r} = r$. Since these two parts are connected in series between points $a$ and $b$, the total equivalent resistance is $R_{eq} = R_1 + R_2 = r + r = 2r$.

The equivalent resistance between the points $a$ and $b$ of the electrical network shown in the figure is:

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