Question

The circuit shown 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 $\frac{R}{5}$

If you carefully see the circuit, the one end of each resistor is connected to A and other end connected to B. Thus the five resistor are in parallel. The equivalent circuit is shown in figure.
Equivalent resistance is $R_{AB}=(\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}{)}^{-1}=\frac{R}{5}$