Question

The circuit showsn has resistors of equal resistance R. Find the equivalent resistance between $A$ and $B$, when the key is closed.

• A. $\frac{11R}{12}$
• B. $\frac{13R}{12}$
• C. $\frac{R}{5}$
• D. $\frac{15R}{12}$

Answer 1

The correct option is C $\frac{R}{5}$

Given,

the resistance of each resistor is $R$.

The circuit shown in the figure can be simplified as figure 1.2 as shown.
This is because all the resistances $1,2,3,4,5$ are connected between potentials $V_A$ and $V_B$.
Resistance $6$ is not considered because it is connected between $V_A$ only. Hence, the potential difference across it is 0.

In figure 1.2, it is clear that all the 5 resistances are in parallel combination.

$\therefore$ The equivalent resistance of the 5 equal resistances connected in parallel is $\frac{R}{5}$

Hence, the answer is $\frac{R}{5}$.