Question

The current (I) drawn from the battery in the given circuit is

• A. 0.2 A
• B. 0.5 A
• C. 0.6 A
• D. 0.8 A

Hint:

Check whether the bridge between B and C is balanced; if so the middle resistor carries no current.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
From the figure, \(A\) to \(B\) is 5 \(\Omega\), \(A\) to \(C\) is 10 \(\Omega\), \(B\) to \(C\) is 10 \(\Omega\), \(B\) to \(D\) is 10 \(\Omega\) and \(C\) to \(D\) is 20 \(\Omega\). This is a bridge.

Step 2: Check the balance
\(\dfrac{R_{AB}}{R_{AC}}=\dfrac{5}{10}=\dfrac{1}{2}\) and \(\dfrac{R_{BD}}{R_{CD}}=\dfrac{10}{20}=\dfrac{1}{2}\).
The bridge is balanced, so no current flows through the 10 \(\Omega\) resistor between B and C.

Step 3: Equivalent resistance
Path A-B-D: \(5+10=15\ \Omega\). Path A-C-D: \(10+20=30\ \Omega\).
In parallel: \(R=\dfrac{15\times30}{45}=10\ \Omega\).

Step 4: Current
\(I=\dfrac{V}{R}=\dfrac{5}{10}=0.5\ \text{A}\).

Final Answer:
The current drawn from the battery is 0.5 A. \[ \boxed{\text{(B) }0.5\ \text{A}} \]