a series RLC circuit has a peak current of 4 A with a frequency of 23 kHz. if the resistance of the circuit is 60 kohm, the capacitance of the circuit is 16 uF, and the unductance of the circuit is 24 uH, determine the average power of the circuit.
Include Steps
I = 0.707 * 4A = 2.83A,rms.
P = I^2 * R = (2.83)^2 * 60,000 =
Answer in Watts.
To determine the average power of the series RLC circuit, we need to calculate the total impedance, the current, and then use the formula for power.
Here are the steps to find the average power of the circuit:
Step 1: Calculate the total impedance (Z) of the circuit using the resistance (R), capacitance (C), and inductance (L).
The impedance (Z) of the circuit is given by:
Z = sqrt((R^2) + (X_L - X_C)^2)
where:
- X_L is the inductive reactance, which is given by 2πfL (2 times pi times the frequency times the inductance).
- X_C is the capacitive reactance, which is given by 1 / (2πfC) (1 divided by 2 times pi times the frequency times the capacitance).
In our case:
- Resistance (R) = 60 kΩ = 60,000 Ω
- Capacitance (C) = 16 uF = 16 x 10^-6 F
- Inductance (L) = 24 uH = 24 x 10^-6 H
- Frequency (f) = 23 kHz = 23 x 10^3 Hz
Using the given values, we can calculate X_L and X_C and then substitute them into the impedance formula to obtain Z.
Step 2: Calculate the current (I) in the circuit.
Given that the peak current is 4 A, we know that the effective or rms (root mean square) current can be calculated as I = (peak current) / √2.
Step 3: Calculate the average power (P) using the formula:
P = I^2 * R
where:
- I is the current in the circuit
- R is the resistance in the circuit
Substitute the calculated values of I and R into the formula to find the average power of the circuit.
By following these steps, you should be able to determine the average power of the given series RLC circuit.