In a Wheatstone bridge, if R1 = 3Ω, R2 = 6Ω, and R3 = 9Ω, what is the value of R

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Question: In a Wheatstone bridge, if R1 = 3Ω, R2 = 6Ω, and R3 = 9Ω, what is the value of R4 for balance?

Options:

Correct Answer: 6Ω

Solution:

Using the balance condition R1/R2 = R3/R4, we find R4 = 6Ω.

In a Wheatstone bridge, if R1 = 3Ω, R2 = 6Ω, and R3 = 9Ω, what is the value of R4 for balance?

In a Wheatstone bridge, if R1 = 3Ω, R2 = 6Ω, and R3 = 9Ω, what is the value of R4 for balance?

Step 1: Write down the given resistances: R1 = 3Ω, R2 = 6Ω, R3 = 9Ω.
Step 2: Use the balance condition formula for a Wheatstone bridge: R1/R2 = R3/R4.
Step 3: Substitute the known values into the formula: 3Ω / 6Ω = 9Ω / R4.
Step 4: Simplify the left side: 3/6 = 1/2.
Step 5: Set up the equation: 1/2 = 9Ω / R4.
Step 6: Cross-multiply to solve for R4: 1 * R4 = 2 * 9Ω.
Step 7: Calculate the right side: R4 = 18Ω.
Step 8: Since we need R4 for balance, we can also rearrange the original balance condition: R4 = (R2 * R3) / R1.
Step 9: Substitute the values: R4 = (6Ω * 9Ω) / 3Ω.
Step 10: Calculate R4: R4 = 54Ω / 3Ω = 18Ω.

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.