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

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Question: In a Wheatstone bridge, if R1 = 10Ω, R2 = 20Ω, and R3 = 30Ω, 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 have 10/20 = 30/R4, which gives R4 = 20Ω.

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

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

Correct Answer: 20Ω

Step 1: Write down the given resistances: R1 = 10Ω, R2 = 20Ω, R3 = 30Ω.
Step 2: Recall the balance condition for a Wheatstone bridge, which is R1/R2 = R3/R4.
Step 3: Substitute the known values into the balance condition: 10/20 = 30/R4.
Step 4: Simplify the left side of the equation: 10/20 = 0.5.
Step 5: Now the equation looks like this: 0.5 = 30/R4.
Step 6: To find R4, cross-multiply: 0.5 * R4 = 30.
Step 7: Divide both sides by 0.5 to solve for R4: R4 = 30 / 0.5.
Step 8: Calculate R4: R4 = 60Ω.

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 the resistances in one leg must equal the ratio in the other leg.