The correct equation for this Wheatstone bridge isa.Rx= R3 (R2 / R1)b.None of thesec.Rx=V R3 (R1 / R2)d.Rx= R3 (R1 / R2)e.Rx=V R3 (R2 / R1)

1. Break Down the Problem

We need to determine the correct equation for the Wheatstone bridge from the provided options. The Wheatstone bridge is used to measure an unknown resistance ($R_x$) in a circuit.

2. Relevant Concepts

The fundamental relationship in a Wheatstone bridge can be expressed as:

$R_x = R_3 \left( \frac{R_2}{R_1} \right)$

This equation balances the bridge when no current flows through the galvanometer.

3. Analysis and Detail

We analyze each option provided:

• Option a: $R_x = R_3 \left( \frac{R_2}{R_1} \right)$ - This matches the formula derived from the Wheatstone bridge.
• Option b: None of these - This cannot be true since option a is correct.
• Option c: $R_x = V R_3 \left( \frac{R_1}{R_2} \right)$ - This doesn’t correspond to any standard formula of a Wheatstone bridge.
• Option d: $R_x = R_3 \left( \frac{R_1}{R_2} \right)$ - This is incorrect as it inversely relates $R_1$ and $R_2$.
• Option e: $R_x = V R_3 \left( \frac{R_2}{R_1} \right)$ - Similar to option c, this is not a correct representation.

4. Verify and Summarize

Based on our analysis, the correct representation of $R_x$ derived from a balanced Wheatstone bridge is found in option a. Other options do not reflect the correct relationship.

Final Answer

The correct equation for the Wheatstone bridge is:
$R_x = R_3 \left( \frac{R_2}{R_1} \right)$ (Option a).