Question

The potential difference between points $A$ and $B$ is:

• A. $\frac{20}{7}V$
• B. $\frac{40}{7}V$
• C. $\frac{10}{7}V$
• D. Zero

Answer 1

Answer: (D)

When resistors are connected in series same current flows through them.
The given circuit can be redrawn as follows:
In this circuit, resistances of $8\Omega$ and $6\Omega$ are connected in series and resistances of $4\Omega$ and $3\Omega$ are also connected in series.
Hence,

$R^{\prime }=8\Omega +6\Omega =14\Omega$
$R^{\prime \prime }=4\Omega +3\Omega =7\Omega$
The given circuit now reduces to as shown:

$i_1=\frac{10}{7}A$
$i_2=\frac{10}{14}A$
From Kirchhoff's law
$V_B-V_A=8i_2-4i_1$
$V_B-V_A=8\times \frac{10}{14}-4\times \frac{10}{7}=0$
Hence, potential difference between points $A$ and $B$ is zero.