Question

Find equivalent resistance between points A and B in the figure when the circuit is in the steady state.

• A. $\frac{3}{4}{r}_0$
• B. $\frac{4}{3}{r}_0$
• C. $\frac{5}{3}{r}_0$
• D. None of these

Answer 1

The correct option is A $\frac{3}{4}{r}_0$

Let us connect the points A and B to a voltage source.
The current distribution in the circuit is as shown


Initially the capacitor will be getting charged due to the current passing through it .
At steady state, the capacitor will be fully charged and no current will flow through this branch.
Now, the simplified circuit diagram will be as shown

The equivalent resistance will be
$R_{eq}=\frac{3r_0{r}_0}{3r_0+r_0}$
$\therefore R_{eq}=\frac{3r_0}{4}$