Question

Колебательный контур содержит конденсатор электроемкостью 8мкФ и катушку индуктивностью 2мГн.Определите резонансную частоту электромагнитных колебаний.

Answer 1

Resonant Frequency of an LC Circuit

To determine the resonant frequency of an LC circuit, we need to consider the values of the capacitor and inductor in the circuit. In this case, the circuit contains a capacitor with a capacitance of 8 μF and an inductor with an inductance of 2 mH.

The resonant frequency of an LC circuit can be calculated using the formula:

Resonant frequency (f) = 1 / (2π√(LC))

where: - f is the resonant frequency in hertz (Hz) - L is the inductance in henries (H) - C is the capacitance in farads (F)

Let's substitute the given values into the formula to calculate the resonant frequency.

Given: - Capacitance (C) = 8 μF = 8 × 10^(-6) F - Inductance (L) = 2 mH = 2 × 10^(-3) H

Calculating the Resonant Frequency: - f = 1 / (2π√(LC)) - f = 1 / (2π√((2 × 10^(-3)) × (8 × 10^(-6))))

Now, let's calculate the resonant frequency using the given values.

f = 1 / (2π√((2 × 10^(-3)) × (8 × 10^(-6)))) f = 1 / (2π√(16 × 10^(-9))) f = 1 / (2π × 4 × 10^(-5)) f ≈ 1 / (2 × 3.14 × 4 × 10^(-5)) f ≈ 1 / (25.12 × 10^(-5)) f ≈ 1 / 0.2512 f ≈ 3.98 Hz

Therefore, the resonant frequency of the given LC circuit is approximately 3.98 Hz.

Please note that the above calculation is based on the given values and the formula for calculating the resonant frequency of an LC circuit.