A 2.0 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF. What is the range of oscillation frequencies for this circuit?

Verified step by step guidance

1. Identify the formula for the resonant frequency of an LC circuit: \( f = \frac{1}{2\pi\sqrt{L C}} \), where \( f \) is the frequency, \( L \) is the inductance, and \( C \) is the capacitance.
2. Convert the given values into standard SI units: \( L = 2.0 \ \text{mH} = 2.0 \times 10^{-3} \ \text{H} \), \( C_{min} = 100 \ \text{pF} = 100 \times 10^{-12} \ \text{F} \), and \( C_{max} = 200 \ \text{pF} = 200 \times 10^{-12} \ \text{F} \).
3. Calculate the minimum frequency using \( C_{max} \): Substitute \( L = 2.0 \times 10^{-3} \ \text{H} \) and \( C = 200 \times 10^{-12} \ \text{F} \) into the formula \( f = \frac{1}{2\pi\sqrt{L C}} \).
4. Calculate the maximum frequency using \( C_{min} \): Substitute \( L = 2.0 \times 10^{-3} \ \text{H} \) and \( C = 100 \times 10^{-12} \ \text{F} \) into the formula \( f = \frac{1}{2\pi\sqrt{L C}} \).
5. The range of oscillation frequencies is from the minimum frequency (calculated with \( C_{max} \)) to the maximum frequency (calculated with \( C_{min} \)).

Key Concepts

Inductance

Inductance is a property of an electrical component, typically a coil or inductor, that quantifies its ability to store energy in a magnetic field when an electric current flows through it. The unit of inductance is the henry (H). In this question, the inductor has a value of 2.0 mH, which will influence the oscillation frequency of the LC circuit.

Capacitance

Capacitance is the ability of a component, usually a capacitor, to store electrical energy in an electric field. It is measured in farads (F). The variable capacitor in this circuit can change its capacitance from 100 pF to 200 pF, affecting the resonant frequency of the circuit when combined with the inductor.

Resonant Frequency

The resonant frequency of an LC circuit is the frequency at which the inductive and capacitive reactances are equal in magnitude, resulting in maximum oscillation. It can be calculated using the formula f = 1/(2π√(LC)), where L is inductance and C is capacitance. This concept is crucial for determining the range of oscillation frequencies for the given inductor and variable capacitor.