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,

$R'=8 \Omega+6 \Omega=14 \Omega$
$R''=4 \Omega+3 \Omega=7 \Omega$
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}=8 i_{2}-4 i_{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.