Question

In a circuit shown, if \(10 \Omega\) resistor is replaced by \(20 \Omega\), then the current drawn from the battery is

• A. 10 A
• B. 4 A
• C. 2 A
• D. 8 A

Hint:

The 3, 8, 9 and 24 ohm resistors form a balanced Wheatstone bridge, so the middle resistor carries no current whatever its value.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In the bridge, the left node connects through 3 \(\Omega\) and 9 \(\Omega\), and the right node through 8 \(\Omega\) and 24 \(\Omega\). The 10 \(\Omega\) resistor joins the two middle nodes.

Step 2: Check Balance
\(\dfrac{3}{9} = \dfrac13\) and \(\dfrac{8}{24} = \dfrac13\), so the bridge is balanced and no current flows through the middle resistor.

Step 3: Effect of Replacing 10 Ohm
Because no current flows through it, changing it to 20 \(\Omega\) does not change the equivalent resistance.
Equivalent \(= \dfrac{11\times 33}{44} = 8.25\ \Omega\), battery emf \(= 4\times 8.25 = 33\ \text{V}\).

Step 4: Result
The current drawn remains 4 A (the value shown in the figure), option B.

Final Answer:
The current drawn from the battery remains 4 A. \[ \boxed{\text{(B) }4\ \text{A}} \]