A series RCL circuit has a resonant frequency of 1530 Hz. When operating at a frequency other than 1530 Hz, the circuit has a capacitive reactance of 5.0 Ω and an inductive reactance of 33.0 Ω.
What is the value of L? (Answer in H)
What it the value of C? (Answer in F)
To find the values of L (inductance) and C (capacitance) in the RCL circuit, we can use the resonant frequency and the reactance values at a different frequency.
Let's start with finding the value of L (inductance):
At the resonant frequency, the reactance of the inductor (XL) and the reactance of the capacitor (XC) cancel out, resulting in a purely resistive circuit. Since the reactances cancel each other out at the resonant frequency, we can set them equal to each other:
XL = XC
Reactance is calculated using the formula:
XL = 2πfL
Where f is the frequency, and L is the inductance.
At the resonant frequency (1530 Hz), the reactance of the inductor is 33.0 Ω. Plugging this value into the reactance formula:
33.0 Ω = 2π * 1530 Hz * L
Now, solve for L:
L = 33.0 Ω / (2π * 1530 Hz)
Calculate the value of L using the formula above.
Next, let's find the value of C (capacitance):
At a frequency other than the resonant frequency, the reactance of the inductor (XL) and the capacitor (XC) are not equal. We can calculate XC using the formula:
XC = 1 / (2πfC)
Where f is the frequency, and C is the capacitance.
At the given frequency, the reactance of the capacitor is 5.0 Ω. Plugging this value into the reactance formula:
5.0 Ω = 1 / (2π * frequency * C)
Now, solve for C:
C = 1 / (2π * frequency * 5.0 Ω)
Calculate the value of C using the formula above.
As a result, you should have the values of L (inductance) and C (capacitance) in the corresponding units (H and F) respectively.