In a Wheatstone bridge, if the known resistances are 5Ω and 10Ω, what is the unknown resistance if the bridge is balanced with a 15Ω resistor?

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Q: In a Wheatstone bridge, if the known resistances are 5Ω and 10Ω, what is the unknown resistance if the bridge is balanced with a 15Ω resistor?

Solution: Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (10 * 15) / 5 = 30Ω.

Steps: 6

Step 1: Identify the known resistances in the Wheatstone bridge. Here, R1 = 5Ω, R2 = 10Ω, and R3 = 15Ω.
Step 2: Use the balance condition formula for a Wheatstone bridge, which is R1/R2 = R3/R4.
Step 3: Rearrange the formula to solve for the unknown resistance R4: R4 = (R2 * R3) / R1.
Step 4: Substitute the known values into the formula: R4 = (10 * 15) / 5.
Step 5: Calculate the value: R4 = 150 / 5 = 30Ω.
Step 6: Conclude that the unknown resistance R4 is 30Ω.