If the resistances in a Wheatstone bridge are R1 = 20Ω, R2 = 30Ω, and R3 = 10Ω,

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Question: If the resistances in a Wheatstone bridge are R1 = 20Ω, R2 = 30Ω, and R3 = 10Ω, what is the value of R4 for the bridge to be balanced?

Options:

Correct Answer: 20Ω

Solution:

Using the balance condition R1/R2 = R3/R4, we have 20/30 = 10/x, solving gives x = 20Ω.

If the resistances in a Wheatstone bridge are R1 = 20Ω, R2 = 30Ω, and R3 = 10Ω, what is the value of R4 for the bridge to be balanced?

If the resistances in a Wheatstone bridge are R1 = 20Ω, R2 = 30Ω, and R3 = 10Ω, what is the value of R4 for the bridge to be balanced?

Correct Answer: 20Ω

Step 1: Write down the resistances given in the problem: R1 = 20Ω, R2 = 30Ω, R3 = 10Ω.
Step 2: Understand the balance condition for a Wheatstone bridge, which is R1/R2 = R3/R4.
Step 3: Substitute the known values into the balance condition: 20/30 = 10/R4.
Step 4: Cross-multiply to eliminate the fraction: 20 * R4 = 30 * 10.
Step 5: Calculate the right side: 30 * 10 = 300.
Step 6: Now you have the equation: 20 * R4 = 300.
Step 7: To find R4, divide both sides by 20: R4 = 300 / 20.
Step 8: Calculate the value: R4 = 15Ω.

Wheatstone Bridge Balance Condition – The Wheatstone bridge is balanced when the ratio of the resistances in one leg equals the ratio in the other leg, expressed as R1/R2 = R3/R4.