Electronics Engineering (ELEX) Board Practice Exam

What is the impedance of a circuit with R = 250 Ω, L = 1.20 mH, C = 1.80 µF at 60 Hz?

1. 1495 Ω

2. 1250 Ω

3. 2000 Ω

4. 1000 Ω

The correct answer is: 1495 Ω

To find the impedance of the circuit, we need to account for the resistance (R), inductive reactance (XL), and capacitive reactance (XC). The impedance in an RLC series circuit can be calculated using the formula: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] Firstly, we calculate the inductive reactance (XL) using the formula: \[ X_L = 2\pi f L \] Where: - f is the frequency in hertz (Hz) - L is the inductance in henries (H) Substituting the values: \[ X_L = 2\pi (60) (1.20 \times 10^{-3}) \] \[ X_L \approx 0.4524 \, \text{Ω} \] Next, we calculate the capacitive reactance (XC) using the formula: \[ X_C = \frac{1}{2\pi f C} \] Where C is the capacitance in farads (F). Substituting the values: \[ X_C = \frac{1}{2\pi (60) (1.80 \times 10^{-6})} \