If the resistances in a Wheatstone bridge are 5Ω, 15Ω, 10Ω, and R, what is the v

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Question: If the resistances in a Wheatstone bridge are 5Ω, 15Ω, 10Ω, and R, what is the value of R for the bridge to be balanced?

Options:

Correct Answer: 12.5Ω

Solution:

Using the balance condition R1/R2 = R3/R4, we find R = (R2 * R3) / R1 = (15 * 10) / 5 = 30Ω.

If the resistances in a Wheatstone bridge are 5Ω, 15Ω, 10Ω, and R, what is the value of R for the bridge to be balanced?

If the resistances in a Wheatstone bridge are 5Ω, 15Ω, 10Ω, 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 = 5Ω, R2 = 15Ω, R3 = 10Ω, and R4 = R (unknown).
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: 5Ω / 15Ω = 10Ω / R.
Step 4: Cross-multiply to eliminate the fraction: 5Ω * R = 15Ω * 10Ω.
Step 5: Calculate the right side: 15 * 10 = 150.
Step 6: Now we have the equation: 5R = 150.
Step 7: Solve for R by dividing both sides by 5: R = 150 / 5.
Step 8: Calculate the value: R = 30Ω.

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, which states that the ratio of the resistances in one leg must equal the ratio in the other leg.
Ohm's Law – The fundamental relationship between voltage, current, and resistance in electrical circuits.