If R1 = 5Ω, R2 = 15Ω, R3 = 10Ω, what should R4 be for the Wheatstone bridge to b

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Question: If R1 = 5Ω, R2 = 15Ω, R3 = 10Ω, what should R4 be for the Wheatstone bridge to be balanced?

Options:

Correct Answer: 10Ω

Solution:

For balance, R4 must be 30Ω since 5/15 = 10/30.

If R1 = 5Ω, R2 = 15Ω, R3 = 10Ω, what should R4 be for the Wheatstone bridge to be balanced?

If R1 = 5Ω, R2 = 15Ω, R3 = 10Ω, what should R4 be for the Wheatstone bridge to be balanced?

Step 1: Understand that a Wheatstone bridge is balanced when the ratio of the resistances in one branch is equal to the ratio in the other branch.
Step 2: Identify the resistances given: R1 = 5Ω, R2 = 15Ω, and R3 = 10Ω.
Step 3: Write the ratio for the first branch (R1 and R2): R1/R2 = 5Ω/15Ω.
Step 4: Simplify the ratio: 5/15 = 1/3.
Step 5: Write the ratio for the second branch (R3 and R4): R3/R4 = 10Ω/R4.
Step 6: Set the two ratios equal to each other for balance: 1/3 = 10/R4.
Step 7: Cross-multiply to solve for R4: 1 * R4 = 3 * 10.
Step 8: Calculate R4: R4 = 30Ω.

Wheatstone Bridge – A circuit used to measure unknown resistances by balancing two legs of a bridge circuit.
Resistance Ratios – The principle that for a Wheatstone bridge to be balanced, the ratio of the resistances in one leg must equal the ratio in the other leg.