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

See previous post.

To determine the average power of the series RLC circuit, you need to follow these steps:

Step 1: Calculate the reactance of the inductor (XL).
Reactance (XL) of an inductor can be calculated using the formula: XL = 2πfL
Where f is the frequency (23 kHz) and L is the inductance (24 μH).

Substituting the values:
XL = 2π × 23,000 Hz × 24 × 10^-6 H

Step 2: Calculate the reactance of the capacitor (XC).
Reactance (XC) of a capacitor can be calculated using the formula: XC = 1 / (2πfC)
Where f is the frequency (23 kHz) and C is the capacitance (16 μF).

Substituting the values:
XC = 1 / (2π × 23,000 Hz × 16 × 10^-6 F)

Step 3: Calculate the impedance (Z) of the circuit.
Impedance (Z) is the total opposition to the flow of current, combining both resistance and reactance.
Z can be calculated using the formula: Z = √((R^2) + ((XL - XC)^2))
Where R is the resistance (60 kΩ), XL is the inductive reactance, and XC is the capacitive reactance.

Substituting the values:
Z = √((60,000 Ω^2) + ((XL - XC)^2))

Step 4: Calculate the average power (Pavg) using the formula: Pavg = (Ipk^2 / 2) × R
Where Ipk is the peak current (4 A) and R is the resistance (60 kΩ).

Substituting the values:
Pavg = (4 A)^2 / 2 × 60,000 Ω

Now let's perform the calculations:

Step 1: Calculate the reactance of the inductor (XL):
XL = 2π × 23,000 Hz × 24 × 10^-6 H

Step 2: Calculate the reactance of the capacitor (XC):
XC = 1 / (2π × 23,000 Hz × 16 × 10^-6 F)

Step 3: Calculate the impedance of the circuit (Z):
Z = √((60,000 Ω^2) + ((XL - XC)^2))

Step 4: Calculate the average power (Pavg):
Pavg = (4 A)^2 / 2 × 60,000 Ω

Performing the calculations will give you the value of the average power of the series RLC circuit.