Question

In a Wheatstone Bridge, all four arms have equal resistance of 1 \(\Omega\) each. A battery is connected across the bridge, and a galvanometer is connected between the middle junctions. What is the current flowing through the galvanometer?

• A. Zero
• B. Depends on battery voltage
• C. Maximum current flows
• D. Cannot be determined

Hint:

Whenever all four resistors in a Wheatstone Bridge are identical, the bridge is always balanced. You don't even need to know the battery voltage to determine that the galvanometer current is zero!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A Wheatstone Bridge is an electrical circuit used to measure an unknown electrical resistance. It consists of four resistances arranged in a diamond shape. The bridge is said to be "balanced" when the potential difference between the middle junctions is zero, resulting in no current flow through the galvanometer.

Step 2: Identifying the Condition for Balance:
For a bridge with arms $P, Q, R,$ and $S$, the balance condition is: \[ \frac{P}{Q} = \frac{R}{S} \] In this state, the galvanometer shows a "null deflection."

Step 3: Detailed Explanation:
In the given problem:
• $P = 1 \, \Omega$
• $Q = 1 \, \Omega$
• $R = 1 \, \Omega$
• $S = 1 \, \Omega$ Calculating the ratios: \[ \frac{P}{Q} = \frac{1}{1} = 1 \] \[ \frac{R}{S} = \frac{1}{1} = 1 \] Since $\frac{P}{Q} = \frac{R}{S}$, the bridge is perfectly balanced. Because the potential at the two junctions where the galvanometer is connected is identical, no potential difference exists to drive a current.

Step 4: Final Answer
The current flowing through the galvanometer is zero.