Question

The equivalent resistance between points $A$ and $B$ with switch $S$ open and closed are respectively

• A. $4\Omega ,8\Omega$
• B. $8\Omega ,4\Omega$
• C. $6\Omega ,9\Omega$
• D. $9\Omega ,6\Omega$

Answer 1

Answer: (B)

When switch $S$ is open, the corresponding equivalent circuit diagram is as shown in the figure.

The equivalent resistance between $A$ and $B$ is
$R_{eq}=\frac{12\times 6}{12+6}+\frac{6\times 12}{6+12}=4+4=8\Omega$
When switch $S$ is closed, the corresponding equivalent circuit diagram is as shown in the figure below

The equivalent resistance between $A$ and $B$ is
$R_{eq}^{\prime }=\frac{8\times 8}{8+8}=4\Omega$