If the resistances in a Wheatstone bridge are 4Ω, 8Ω, 12Ω, and R, what is the va

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Question: If the resistances in a Wheatstone bridge are 4Ω, 8Ω, 12Ω, and R, what is the value of R for the bridge to be balanced?

Options:

Correct Answer: 6Ω

Solution:

Using the balance condition R1/R2 = R3/R4, we find R = (R2 * R3) / R1 = (8 * 12) / 4 = 24Ω.

If the resistances in a Wheatstone bridge are 4Ω, 8Ω, 12Ω, and R, what is the value of R for the bridge to be balanced?

If the resistances in a Wheatstone bridge are 4Ω, 8Ω, 12Ω, and R, what is the value of R for the bridge to be balanced?

Step 1: Identify the resistances in the Wheatstone bridge. We have R1 = 4Ω, R2 = 8Ω, R3 = 12Ω, and R4 = R (the unknown resistance).
Step 2: Write down the balance condition for a Wheatstone bridge, which is R1/R2 = R3/R4.
Step 3: Substitute the known values into the balance condition: 4Ω / 8Ω = 12Ω / R.
Step 4: Cross-multiply to eliminate the fraction: 4Ω * R = 8Ω * 12Ω.
Step 5: Calculate the right side: 8 * 12 = 96. So, we have 4R = 96.
Step 6: Solve for R by dividing both sides by 4: R = 96 / 4.
Step 7: Calculate the final value: R = 24Ω.

Wheatstone Bridge – A circuit used to measure unknown resistances by balancing two legs of a bridge circuit.
Balance Condition – The condition for a Wheatstone bridge to be balanced is that the ratio of the resistances in one leg equals the ratio in the other leg.
Ohm's Law – The relationship between voltage, current, and resistance, which underlies the operation of the Wheatstone bridge.