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If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, and R
If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, and R4 = xΩ, what value of x will balance the bridge?
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Practice Questions
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Q1
If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, and R4 = xΩ, what value of x will balance the bridge?
7.5Ω
10Ω
12.5Ω
15Ω
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Using the balance condition R1/R2 = R3/R4, we have 10/15 = 5/x, solving gives x = 7.5Ω.
Questions & Step-by-step Solutions
1 item
Q
Q: If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, and R4 = xΩ, what value of x will balance the bridge?
Solution:
Using the balance condition R1/R2 = R3/R4, we have 10/15 = 5/x, solving gives x = 7.5Ω.
Steps: 7
Show Steps
Step 1: Write down the resistances given in the problem: R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, and R4 = xΩ.
Step 2: Understand the balance condition for a Wheatstone bridge, which is R1/R2 = R3/R4.
Step 3: Substitute the known values into the balance condition: 10/15 = 5/x.
Step 4: Cross-multiply to eliminate the fraction: 10 * x = 15 * 5.
Step 5: Calculate the right side: 15 * 5 = 75, so now we have 10 * x = 75.
Step 6: Solve for x by dividing both sides by 10: x = 75 / 10.
Step 7: Calculate the final value: x = 7.5Ω.
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