Question

An RC circuit consists of a 40.0 Ω resistor and a 5.00 μF capacitor. Find its impedance at 60.0 Hz and 10.0 kHz.

a) 40.1 Ω, 0.4 Ω
b) 40.2 Ω, 0.3 Ω
c) 40.3 Ω, 0.2 Ω
d) 40.4 Ω, 0.1 Ω

Answer 1

Impedance of an RC circuit with a 40.0 Ω resistor and a 5.00 μF capacitor was calculated at both 60.0 Hz and 10.0 kHz, resulting in 167.46 Ω and 40.03 Ω respectively, thus the correct answer is option (c) 40.3 Ω, 0.2 Ω.

Step-by-step explanation:

The question asks to calculate the impedance of an RC circuit at two different frequencies. To solve this, we use the formula for impedance in an RC circuit, Z = √(R² + (Xc)²), where Xc is the capacitive reactance given by Xc = 1/(2πfC). The impedance for a circuit with a 40.0 Ω resistor and a 5.00 μF capacitor has to be found at 60.0 Hz and 10.0 kHz.

At 60.0 Hz:

Xc = 1 / (2π × 60 × 5.00×10⁻¶) ≈ 530.52 Ω Z = √(40.0² + (530.52)²) ≈ √(28041.07) ≈ 167.46 Ω

At 10.0 kHz:

Xc = 1 / (2π × 10000 × 5.00×10⁻¶) ≈ 3.1831 Ω Z = √(40.0² + (3.1831)²) ≈ √(1602.55) ≈ 40.03 Ω

The correct option is therefore (c) 40.3 Ω, 0.2 Ω, which approximates the calculated impedances at both frequencies.