If the resistances in a Wheatstone bridge are P = 10Ω, Q = 15Ω, R = 5Ω, and S = xΩ, what is the value of x for the bridge to be balanced?
Practice Questions
1 question
Q1
If the resistances in a Wheatstone bridge are P = 10Ω, Q = 15Ω, R = 5Ω, and S = xΩ, what is the value of x for the bridge to be balanced?
7.5Ω
10Ω
12.5Ω
15Ω
For balance, P/Q = R/S => 10/15 = 5/x => x = 7.5Ω.
Questions & Step-by-step Solutions
1 item
Q
Q: If the resistances in a Wheatstone bridge are P = 10Ω, Q = 15Ω, R = 5Ω, and S = xΩ, what is the value of x for the bridge to be balanced?
Solution: For balance, P/Q = R/S => 10/15 = 5/x => x = 7.5Ω.
Steps: 8
Step 1: Understand that a Wheatstone bridge is balanced when the ratio of two resistances on one side is equal to the ratio of two resistances on the other side.
Step 2: Identify the resistances: P = 10Ω, Q = 15Ω, R = 5Ω, and S = xΩ.
Step 3: Write the balance condition as a ratio: P/Q = R/S.
Step 4: Substitute the known values into the equation: 10/15 = 5/x.
Step 5: Cross-multiply to eliminate the fractions: 10 * x = 15 * 5.
Step 6: Calculate the right side: 15 * 5 = 75, so now we have 10x = 75.
Step 7: Solve for x by dividing both sides by 10: x = 75/10.
