CSLB C-10 Electrical ContractorElectrical Theory and CalculationsMedium
A parallel circuit has three resistors: R1 = 10 ohms, R2 = 15 ohms, and R3 = 30 ohms. What is the total resistance of this parallel circuit?
- A55 ohms
- B3 ohms
- C5 ohms
- D10 ohms
Show answer & explanationAnswer & explanation
Correct answer: C. 5 ohms
For resistors in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances (1/Rt = 1/R1 + 1/R2 + 1/R3).
Why the other options are wrong
- A. This is a calculation error, summing the resistances as if they were in series.
- B. This is a calculation error, possibly an incorrect reciprocal sum.
- D. This is a calculation error, possibly taking the lowest individual resistance.
Parallel Circuit Total Resistance
In a parallel circuit, components are connected across the same two points, sharing the same voltage. The total resistance is always less than the smallest individual resistance.
- Formula: 1/Rt = 1/R1 + 1/R2 + 1/R3 + ...
- Voltage is the same across all parallel components.
- Current divides among the branches.
Memory trick: Parallel is 'P' for 'Product-over-Sum' (for two) or 'Reciprocal Sum' (for many).