Question

What inductance is required for a resonant frequency of 60.0 Hz when paired with a 2.00 μF capacitor?

a) 2.65 H
b) 1.59 H
c) 0.95 H
d) 0.53 H

Answer 1

To achieve a resonant frequency of 60.0 Hz with a 2.00 μF capacitor, an inductance of 1.59 H is required. This is calculated using the resonant frequency formula for an LC circuit. Therefore, the correct option is b).

Step-by-step explanation:

The question involves finding the inductance needed for a circuit to resonate at a specific frequency when paired with a known capacitance. A resonant circuit containing an inductor and a capacitor (LC circuit) will oscillate at its resonant frequency, which is determined by the formula ω = 1/√(LC), where ω is the angular frequency, L is the inductance, and C is the capacitance. In this problem, the resonant frequency (f) is given as 60.0 Hz and the capacitance (C) is 2.00 μF. The angular frequency is related to the frequency by the formula ω = 2πf.

First, we convert the frequency to angular frequency: ω = 2π × 60.0 Hz = 376.99 rad/s. Then, using the formula for resonant frequency, we can solve for inductance (L): L = 1/(ω²C). Plugging in the values for ω and C, we get L = 1 / ((376.99 rad/s)² × 2.00 μF) = 1.59 H. Therefore, the required inductance is 1.59 H, making the correct option (b).