Ignoring any effects of dc resistance, what is the total reactance of a 250 mH coil in series with a 4.7 microfarad capacitor at

Question

2 years ago

10

a signal frequency of 60 Hz

1 answer:

Paha777 [63] · Answer 1 · 2023-03-12T01:22:25+03:00

The total reactance of the inductor and the capacitor is 470.1 ohms.

The given parameters;

The inductive reactance of the coil is calculated as follows;

$X_l = \omega L\\\\X_l = 2\pi f L\\\\X_l = 2\pi \times 60 \times 250 \times 10^{-3}\\\\X_l = 94.26 \ ohms$

The capacitive reactance of the capacitor is calculated as follows;

$X_c = \frac{1}{\omega C} \\\\X_c = \frac{1}{2\pi f C} \\\\X_c = \frac{1}{2\pi \times 60 \times 4.7 \times 10^{-6}} \\\\X_c = 564.31 \ ohms$

The impedance of the circuit is calculated as follows;

$Z = \sqrt{(X_c - X_l)^2} \\\\Z = X_c - X_l\\\\Z = 564.31 - 94.26\\\\Z = 470.1 \ ohms$

Thus, the total reactance of the inductor and the capacitor is 470.1 ohms.