In a Wheatstone bridge, if R1 = 4Ω, R2 = 6Ω, and R3 = 12Ω, what is the value of

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Question: In a Wheatstone bridge, if R1 = 4Ω, R2 = 6Ω, and R3 = 12Ω, what is the value of R4 for the bridge to be balanced?

Options:

Correct Answer: 12Ω

Solution:

Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (6 * 12) / 4 = 18Ω.

In a Wheatstone bridge, if R1 = 4Ω, R2 = 6Ω, and R3 = 12Ω, what is the value of R4 for the bridge to be balanced?

In a Wheatstone bridge, if R1 = 4Ω, R2 = 6Ω, and R3 = 12Ω, what is the value of R4 for the bridge to be balanced?

Step 1: Write down the values of the resistors: R1 = 4Ω, R2 = 6Ω, R3 = 12Ω.
Step 2: Recall the balance condition for a Wheatstone bridge, which is R1/R2 = R3/R4.
Step 3: Rearrange the balance condition to solve for R4: R4 = (R2 * R3) / R1.
Step 4: Substitute the values into the equation: R4 = (6 * 12) / 4.
Step 5: Calculate the multiplication: 6 * 12 = 72.
Step 6: Divide the result by R1: 72 / 4 = 18.
Step 7: Conclude that the value of R4 for the bridge to be balanced is 18Ω.

Wheatstone Bridge – A circuit used to measure unknown electrical 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.