In a Wheatstone bridge, if R1 = 10Ω, R2 = 15Ω, and R3 = 30Ω, what is the value o

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Question: In a Wheatstone bridge, if R1 = 10Ω, R2 = 15Ω, and R3 = 30Ω, what is the value of R4 for the bridge to be balanced?

Options:

Correct Answer: 25Ω

Solution:

Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (15 * 30) / 10 = 45Ω.

In a Wheatstone bridge, if R1 = 10Ω, R2 = 15Ω, and R3 = 30Ω, what is the value of R4 for the bridge to be balanced?

In a Wheatstone bridge, if R1 = 10Ω, R2 = 15Ω, and R3 = 30Ω, what is the value of R4 for the bridge to be balanced?

Step 1: Understand that a Wheatstone bridge is balanced when the ratio of the resistances is equal. This means R1/R2 = R3/R4.
Step 2: Identify the given values: R1 = 10Ω, R2 = 15Ω, R3 = 30Ω.
Step 3: Write down the balance condition: R1/R2 = R3/R4.
Step 4: Rearrange the equation to solve for R4: R4 = (R2 * R3) / R1.
Step 5: Substitute the known values into the equation: R4 = (15 * 30) / 10.
Step 6: Calculate the multiplication: 15 * 30 = 450.
Step 7: Divide the result by R1: 450 / 10 = 45.
Step 8: Conclude that the value of R4 for the bridge to be balanced is 45Ω.

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 is that the ratio of the resistances in one leg equals the ratio in the other leg (R1/R2 = R3/R4).
Ohm's Law – The relationship between voltage, current, and resistance, which underlies the operation of the Wheatstone bridge.