CSLB C-10 Electrical ContractorElectrical Theory and CalculationsMedium
A technician is troubleshooting a 120V AC circuit that includes a capacitor. If the capacitor has a capacitance of 50 µF and the circuit operates at 60 Hz, what is the approximate capacitive reactance (Xc) of the capacitor?
- A0.0053 ohms
- B188.5 ohms
- C53.05 ohms
- D377.0 ohms
Show answer & explanationAnswer & explanation
Correct answer: C. 53.05 ohms
Capacitive reactance (Xc) is calculated using the formula Xc = 1 / (2πfC). Given f = 60 Hz and C = 50 µF (0.000050 F), Xc = 1 / (2π × 60 Hz × 0.000050 F) ≈ 53.05 ohms.
Why the other options are wrong
- A. This value is significantly too small, likely a calculation error or unit conversion mistake.
- B. This value might arise from an incorrect formula or unit conversion, possibly related to inductive reactance.
- D. This is approximately the inductive reactance of an inductor with a specific inductance, not capacitive reactance.
Capacitive Reactance
Capacitive reactance (Xc) is the opposition a capacitor offers to the flow of alternating current (AC). It is inversely proportional to both the capacitance and the frequency.
- Formula: Xc = 1 / (2πfC)
- Measured in Ohms (Ω).
- Causes current to lead voltage by 90 degrees in a purely capacitive circuit.
Memory trick: Capacitors Resist Current, but Reactance is 1 over 2 Pi FC.