Question

In a Wheatstone bridge, the bridge is balanced when the ratio of the resistances in the four arms satisfies

• A. $P/Q = R/S$
• B. $P/R = S/Q$
• C. $PS = QR$
• D. $P+Q = R+S$

Hint:

Remember that in a balanced Wheatstone bridge, the product of the resistances on one pair of opposite arms is equal to the product of the resistances on the other pair.

Answer 1

The Correct Option is A

Step 1: Understand the bridge.
A Wheatstone bridge has four resistors $P$, $Q$, $R$, and $S$ arranged in a diamond. A galvanometer sits across the middle to detect current.

Step 2: Know what balanced means.
The bridge is balanced when no current flows through the galvanometer. This happens when the two middle points are at the same potential.

Step 3: Write the balance rule.
When balanced, the ratio of resistances in the two arms on one side equals the ratio on the other side. \[ \frac{P}{Q} = \frac{R}{S} \]

Step 4: Rearrange the relation.
Cross multiplying gives the product form. \[ PS = QR \] Both forms describe the same balance condition.

Step 5: Check the matching option.
The option that exactly states $P/Q = R/S$ is the direct balance condition asked for.

Step 6: State the answer.
The bridge balances when the arm ratios are equal. \[ \boxed{\frac{P}{Q} = \frac{R}{S}} \]