Question

An l-r-c series circuit consists of a source with voltage amplitude 120 v and angular frequency 50.0 rad/s , a resistor with r = 400 �� , an inductor with l = 3.00 h , and a capacitor with capacitance c . What is the value of capacitance c?

Answer 1

To find the capacitance C in the RLC series circuit, use the formula C = 1 / (ω^2L) with the provided values. Substituting ω = 50.0 rad/s and L = 3.00 H gives C = 1.33 x 10^-4 F or 133 μF.

Step-by-step explanation:

To calculate the value of the capacitance C in an RLC series circuit with a given resistor (R), inductor (L), and voltage amplitude of the AC source, we need to use the formula for the resonant frequency at which the inductive reactance XL and capacitive reactance XC are equal but opposite in phase, effectively canceling each other out. This resonant frequency f0 is given by:

f0 = 1 / (2π√(LC))

The angular frequency ω is given, which is related to the resonant frequency by ω = 2πf0. The value of angular frequency ω is 50.0 rad/s, and the inductor L is 3.00 H. We can then rearrange the above resonance frequency formula to solve for C:

C = 1 / (ω2L)

Inserting the given values:

C = 1 / ((50.02)(3.00))

C = 1 / (2500 * 3)

C = 1 / 7500

C = 1.33 x 10-4 F or 133 μF (microfarads).