Get Wired 102 Introduction To The Basic Installation Of Lighting Fixtures And Branch Circuits Practice Test

A two-branch parallel circuit has a 30 ohm and a 15 ohm resistor. What is the total resistance?

45 ohms 25 ohms 60 ohms 10 ohms

Correct Answer:

10 ohms

Explanation:

In a parallel circuit, the total resistance comes from adding the reciprocals of each branch and then taking the reciprocal of that sum. For two resistors, 1/Rt = 1/R1 + 1/R2. Plugging in 30 ohms and 15 ohms: 1/Rt = 1/30 + 1/15 = 1/30 + 2/30 = 3/30 = 1/10. Inverting gives Rt = 10 ohms. This fits the general rule that the total resistance in parallel is always less than the smallest individual resistance, which here is 15 ohms, so 10 ohms makes sense. The other options don’t fit: 45 ohms would be the sum of the resistors (series), 60 ohms isn’t achievable with these values in parallel, and 25 ohms would be greater than the smallest resistor, which isn’t possible in parallel.

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