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 consists of four resistors $R_1, R_2, R_3,$ and $R_4$ arranged in a quadrilateral shape. A galvanometer is connected between the middle junctions. The bridge is said to be "balanced" when the ratio of the resistances in the opposite arms is equal.
Step 2: Key Formula or Approach:
The balancing condition for a Wheatstone bridge is given by $\frac{R_1}{R_2} = \frac{R_3}{R_4}$. When this condition is met, the potential difference across the galvanometer terminals becomes zero, and by Ohm's Law ($I = \frac{V}{R}$), the current through the galvanometer is zero.
Step 3: Detailed Explanation:
Given that all four arms have an equal resistance of $1\ \Omega$: \[ \frac{R_1}{R_2} = \frac{1}{1} = 1 \] \[ \frac{R_3}{R_4} = \frac{1}{1} = 1 \] Since $\frac{R_1}{R_2} = \frac{R_3}{R_4}$, the Wheatstone bridge is perfectly balanced.
Therefore, the potential at the two junctions connecting the galvanometer is identical ($\Delta V = 0$). As a result, no current flows through the galvanometer.
Step 4: Final Answer:
The current flowing through the galvanometer is zero.