Question

The value of current \(I\) in the electrical circuit as given below, when potential at \(A\) is equal to the potential at \(B\), will be _____ A. graphics[width=0.5\linewidth]{Q5.png}

• A. \(2A\)
• B. \(3A\)
• C. \(4A\)
• D. \(5A\)

Hint:

For a balanced Wheatstone bridge: \[ \frac{P}{Q}=\frac{R}{S} \] No current flows through the middle branch.

Answer 1

The Correct Option is C

Step 1: Use the condition \(V_A = V_B\).
Since: \[ V_A=V_B \] no current flows through the \(30\Omega\) resistor. Hence, the bridge is balanced.

Step 2: Apply Wheatstone bridge condition.
For balanced bridge: \[ \frac{10}{20}=\frac{R}{40} \] \[ \frac{1}{2}=\frac{R}{40} \] \[ R=20\Omega \]

Step 3: Find equivalent resistance.
Upper branch resistance: \[ 10+20=30\Omega \] Lower branch resistance: \[ 20+40=60\Omega \] These two branches are in parallel. So: \[ R_{\text{eq}}=\frac{30\times 60}{30+60} \] \[ R_{\text{eq}}=\frac{1800}{90} \] \[ R_{\text{eq}}=20\Omega \]

Step 4: Apply Ohm's Law.
Given battery voltage: \[ V=40V \] Current: \[ I=\frac{V}{R_{\text{eq}}} \] \[ I=\frac{40}{20} \] \[ I=2A \]

Step 5: Identify the correct option.
Therefore: \[ \boxed{I=2A} \] Hence, the correct answer is: \[ \boxed{\mathrm{(A)}} \]