CSLB C-10 Electrical ContractorElectrical Theory and CalculationsMedium
A parallel circuit contains three resistors: R1 = 100 ohms, R2 = 200 ohms, and R3 = 400 ohms. What is the total equivalent resistance of this circuit?
- A33.33 ohms
- B40 ohms
- C57.14 ohms
- D700 ohms
Show answer & explanationAnswer & explanation
Correct answer: C. 57.14 ohms
For parallel resistors, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances: 1/Rt = 1/R1 + 1/R2 + 1/R3. So, 1/Rt = 1/100 + 1/200 + 1/400 = 0.01 + 0.005 + 0.0025 = 0.0175. Therefore, Rt = 1 / 0.0175 ≈ 57.14 ohms.
Why the other options are wrong
- A. This might be a calculation error or an average of the resistances.
- B. This could be a result of incorrectly applying the parallel resistance formula.
- D. This is the sum of resistors, which is for series circuits.
Parallel Resistance Total
The total resistance of resistors in parallel is calculated by summing the reciprocals of individual resistances and then taking the reciprocal of that sum.
- 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn
- Total resistance is always less than the smallest individual resistor.
- Current divides among parallel branches.
Memory trick: Parallel paths means reciprocal sums, making total smaller.