If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what

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Question: If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what is the value of R4 for the bridge to be balanced?

Options:

Correct Answer: 12.5Ω

Solution:

Using the balance condition R1/R2 = R3/R4, we have 10/15 = 5/R4. Solving gives R4 = 7.5Ω.

If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what is the value of R4 for the bridge to be balanced?

If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what is the value of R4 for the bridge to be balanced?

Correct Answer: 7.5Ω

Step 1: Write down the resistances given in the problem: R1 = 10Ω, R2 = 15Ω, R3 = 5Ω.
Step 2: Recall the balance condition for a Wheatstone bridge, which is R1/R2 = R3/R4.
Step 3: Substitute the known values into the balance condition: 10/15 = 5/R4.
Step 4: To solve for R4, cross-multiply: 10 * R4 = 15 * 5.
Step 5: Calculate 15 * 5, which equals 75: 10 * R4 = 75.
Step 6: Now, divide both sides by 10 to isolate R4: R4 = 75 / 10.
Step 7: Calculate 75 / 10, which equals 7.5Ω.
Step 8: Conclude that the value of R4 for the bridge to be balanced is 7.5Ω.

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.