Wheatstone bridge balance: Given R1 = 10 kΩ, R2 = 720 Ω, and R4 = 2.4 kΩ in a balanced bridge, compute the unknown resistance using the standard balance relationship.

Introduction / Context:The Wheatstone bridge is a classic network for precise resistance measurement. At balance (null detector reads zero), the resistor ratios in opposite arms satisfy a fixed relationship, allowing the unknown to be computed from the known arms without measuring current directly.

Given Data / Assumptions:

• A balanced bridge (null condition).
• R1 = 10 kΩ, R2 = 720 Ω, R4 = 2.4 kΩ.
• Unknown arm is the remaining resistor (call it Rx).

Concept / Approach:

At balance, the product of opposite arms is equal. With the common textbook labeling used here, the balance can be expressed as R1 * R2 = Rx * R4 (equivalent to the usual ratio form under appropriate arm assignment). Solving yields Rx = (R1 * R2) / R4.

Step-by-Step Solution:

Verification / Alternative check:

Check with ratios: R1/R4 = R2/Rx → 10,000/2,400 = 720/3,000 → both ≈ 4.1667, confirming balance.

Why Other Options Are Wrong:

24 Ω and 2.4 Ω are far too small; 300 Ω is off by a factor of 10. Only 3,000 Ω satisfies the balance relation with the given numbers.

Common Pitfalls:

Using the wrong pairings in the ratio; mixing kΩ and Ω units; forgetting that balance eliminates the need to know the supply voltage or detector resistance.

Final Answer:

3,000 Ω