Question

The potential difference between $A$ and $B$ as shown in figure is

• A. $1V$
• B. $2V$
• C. $3V$
• D. $4V$

Answer 1

Answer: (A)

Resistance of the upper arm
$CAD=2\Omega +3\Omega =5\Omega$
Resistance of the lower arm
$CBD=3\Omega +2\Omega =5\Omega$

As the resistance of both arms are equal, therefore same amount of current flows in both the arms. Current through each arm
$CAD$ or $CBD=1A$

Potential difference across $C$ and $A$ is
$V_C-V_A=\left(2\Omega \right)\left(1A\right)=2V\dots \left(i\right)$
Potential difference across $C$ and $B$ is
$V_C-V_B=\left(3\Omega \right)\left(1A\right)=3V\dots \left(ii\right)$
Subtracting $\left(i\right)$ from $\left(ii\right)$, we get
$V_A-V_B=3V-2V=1V$