Question

What is the resonant frequency of a 0.500 mH inductor connected to a 40.0 μF capacitor?

a. 10.0 Hz
b. 40.0 Hz
c. 20.0 Hz
d. 5.00 Hz

Answer 1

The correct answer is 20.0 Hz because it is the resonant frequency calculated using the inductance and capacitance values provided in the circuit. So the correct option is c. 20.0 Hz.

Step-by-step explanation:

The resonant frequency of the given inductor-capacitor circuit can be calculated using the formula:

`\[f_{\text{res}} = (1)/(2\pi√(LC))\]`

Where:

`\(f_{\text{res}}\)` = resonant frequency

`\(L\)` = inductance in henrys (H)

`\(C\)` = capacitance in farads (F)

In this case, the inductance
`(\(L\))` is given as 0.500 mH, which is equivalent to 0.0005 H, and the capacitance
`(\(C\))` is 40.0 μF, equivalent to 0.000040 F. Substituting these values into the formula:

`\[f_{\text{res}} = (1)/(2\pi√((0.0005)(0.000040)))\]`

Calculating the expression gives a resonant frequency
`(\(f_{\text{res}}\))` of approximately 20.0 Hz. Therefore, the correct option is c. 20.0 Hz.

This resonant frequency represents the frequency at which the inductive and capacitive reactances are equal, resulting in resonance. At this frequency, the impedance of the circuit is minimized, and the current through the circuit is maximized. Understanding the resonant frequency is crucial in designing and analyzing circuits, especially in applications like filters and tuning circuits.