In a Wheatstone bridge, if R1 = 20Ω, R2 = 30Ω, and R3 = 10Ω, what is the value o

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Question: In a Wheatstone bridge, if 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 find R4 = (R2 * R3) / R1 = (30 * 10) / 20 = 15Ω.

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

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

Step 1: Understand the Wheatstone bridge balance condition, which states that R1/R2 = R3/R4.
Step 2: Identify the values given: R1 = 20Ω, R2 = 30Ω, and R3 = 10Ω.
Step 3: Rearrange the balance condition formula to solve for R4: R4 = (R2 * R3) / R1.
Step 4: Substitute the values into the formula: R4 = (30 * 10) / 20.
Step 5: Calculate the numerator: 30 * 10 = 300.
Step 6: Divide the result by R1: 300 / 20 = 15.
Step 7: Conclude that the value of R4 for the bridge to be balanced is 15Ω.

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 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.