In a Wheatstone bridge, if P = 20Ω, Q = 30Ω, and R = 10Ω, what is the value of S

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Question: In a Wheatstone bridge, if P = 20Ω, Q = 30Ω, and R = 10Ω, what is the value of S for the bridge to be balanced?

Options:

Correct Answer: 20Ω

Solution:

Using the balance condition P/Q = R/S, we find S = 15Ω.

In a Wheatstone bridge, if P = 20Ω, Q = 30Ω, and R = 10Ω, what is the value of S for the bridge to be balanced?

In a Wheatstone bridge, if P = 20Ω, Q = 30Ω, and R = 10Ω, what is the value of S for the bridge to be balanced?

Step 1: Write down the given values: P = 20Ω, Q = 30Ω, R = 10Ω.
Step 2: Recall the balance condition for a Wheatstone bridge, which is P/Q = R/S.
Step 3: Substitute the known values into the balance condition: 20Ω / 30Ω = 10Ω / S.
Step 4: Cross-multiply to eliminate the fraction: 20Ω * S = 30Ω * 10Ω.
Step 5: Calculate the right side: 30Ω * 10Ω = 300Ω.
Step 6: Now you have the equation: 20Ω * S = 300Ω.
Step 7: Solve for S by dividing both sides by 20Ω: S = 300Ω / 20Ω.
Step 8: Calculate the value of S: S = 15Ω.

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 given by the ratio of the resistances in one leg being equal to the ratio in the other leg.