Question

When some potential difference is maintained between $A$ and $B$, current i enters the network at $A$ and leaves at $B$ as shown in the figure. Then
(1) The equivalent resistance between $A$ and $B$ is $8 \Omega$.
(2) $C$ and $D$ are at the same potential
(3) Current $\frac{3 i}{5}$ flows from $D$ to $C$
(4) No current flows between $C$ and $D$

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (A)

The equivalent resistance between points $A$ and $B$ is

$R_{e q}=\frac{20 \times 5}{20+5}+\frac{5 \times 20}{5+20}$
$R_{e q}=8 \Omega $
$C$ and $D$ are joined, they must be at the same potential.

$V_{A}-V_{C}=V_{A}-V_{D} $
$20 i_{1}=5\left(i-i_{1}\right)$
$i_{1}=\frac{i}{5}$
Current flowing from $D$ to $C$ is
$i-2 i_{1}=i-\frac{2 i}{5}=\frac{3 i}{5}$