Question

An rlc circuit has a 24 ω resistor and a 58 μh inductor; when connected to an ac source, its resonance frequency is 320 khz .

Answer 1

To find the capacitance, rearrange the formula and solve for C using the given resonance frequency and inductance.

Step-by-step explanation:

In an RLC circuit, the resonance frequency is the frequency at which the inductive reactance cancels out the capacitive reactance, resulting in a purely resistive impedance. To find the resonance frequency, we can use the formula:

fr = 1 / (2π√(LC))

where fr is the resonance frequency, L is the inductance, and C is the capacitance. Given the inductance L = 58 μH and the capacitance C = unknown, we can rearrange the formula to solve for C:

C = 1 / (4π²L(fr)²)

Using the given resonance frequency fr = 320 kHz and substituting the values into the formula, we can calculate the capacitance:

C = 1 / (4π²(58 μH)(320 kHz)²)

Solving this equation will give us the value of C in farads.