If R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω in a Wheatstone bridge, what is the value of R4

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Question: If R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω in a Wheatstone bridge, what is the value of R4 for balance?

Options:

Correct Answer: 4Ω

Solution:

Using the balance condition R1/R2 = R3/R4, we have 2/3 = 6/R4. Solving gives R4 = 4Ω.

If R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω in a Wheatstone bridge, what is the value of R4 for balance?

If R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω in a Wheatstone bridge, what is the value of R4 for balance?

Correct Answer: 4Ω

Step 1: Identify the resistances in the Wheatstone bridge. We have R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω.
Step 2: Write down the balance condition for the Wheatstone bridge, which is R1/R2 = R3/R4.
Step 3: Substitute the known values into the balance condition: 2/3 = 6/R4.
Step 4: To solve for R4, cross-multiply: 2 * R4 = 3 * 6.
Step 5: Calculate the right side: 3 * 6 = 18, so we have 2 * R4 = 18.
Step 6: Divide both sides by 2 to isolate R4: R4 = 18 / 2.
Step 7: Calculate the final value: R4 = 9Ω.

Wheatstone Bridge Balance Condition – The balance condition of a Wheatstone bridge states that the ratio of the resistances in one branch is equal to the ratio of the resistances in the other branch.