CSLB C-10 Electrical ContractorElectrical Theory and CalculationsMedium
A parallel circuit has three resistors: R1 = 60 ohms, R2 = 30 ohms, and R3 = 20 ohms. What is the total equivalent resistance of this parallel combination?
- A600 ohms
- B5 ohms
- C110 ohms
- D10 ohms
Show answer & explanationAnswer & explanation
Correct answer: D. 10 ohms
For parallel resistors, the reciprocal of the total resistance is the sum of the reciprocals: 1/Rt = 1/R1 + 1/R2 + 1/R3. So, 1/Rt = 1/60 + 1/30 + 1/20 = 1/60 + 2/60 + 3/60 = 6/60 = 1/10. Therefore, Rt = 10 ohms.
Why the other options are wrong
- A. This is a significantly incorrect value, possibly from multiplying resistances instead of using reciprocals.
- B. This is a common error, possibly from incorrect addition of fractions or calculation.
- C. This would be the total resistance if the resistors were in series.
Parallel Resistive Circuit (Total Resistance)
In a parallel resistive circuit, the reciprocal of the total equivalent resistance is equal to the sum of the reciprocals of the individual resistances.
- Formula: 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn.
- The total resistance in a parallel circuit is always less than the smallest individual resistance.
- For two resistors: Rt = (R1 * R2) / (R1 + R2).
- Voltage is the same across all branches.
Memory trick: Reciprocal sum for parallel, less than the smallest for all.