A series RLC circuit has an impedance of 120ohm and a resistance of 64ohm. What maximum power is delivered to this circuit when Vrms = 90 volts?
A series RLC circuit has an impedance of 120ohms and a resistance of 64ohms. What average power is delivered to this circuit when Vrms = 90 volts?
I = E/Z = 90/120 = 0.75A.
P = I^2*R = 0.75^2 * 64 = ___ Watts.
Find the resonant frequency for a series RLC circuit where R = 10ohms, C = 5.00 uF, and L = 2.00 mH.
2
To determine the maximum power delivered to the series RLC circuit, you first need to find the value of the maximum current flowing through the circuit, which will then dictate the maximum power consumption using the formula P = I^2 * R.
The given impedance of the series RLC circuit is 120 ohms, and the resistance is 64 ohms. The impedance of a series RLC circuit can be calculated using the formula Z = sqrt(R^2 + (Xl - Xc)^2), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance.
Since the circuit is described as a series RLC circuit, it can be assumed that it consists of a resistor (R), an inductor (L), and a capacitor (C), each with their respective reactances.
Given that the resistance value is 64 ohms, we can substitute this into the formula:
Z = sqrt(64^2 + (Xl - Xc)^2)
Now, we can rearrange the formula to solve it for Xl - Xc:
(Xl - Xc)^2 = Z^2 - R^2
(Xl - Xc)^2 = 120^2 - 64^2
(Xl - Xc)^2 = 14400 - 4096
(Xl - Xc)^2 = 10304
Xl - Xc = sqrt(10304)
Xl - Xc = 101.5 ohms
The given maximum voltage (Vrms) is 90 volts, which will be the peak voltage of the circuit. The peak current (Ipk) can be calculated using the formula Ipk = Vpk / Z, where Vpk is the peak voltage and Z is the impedance.
For our calculations, we need to convert the peak voltage (Vpk) to Vrms, which is done by dividing it by the square root of 2. Therefore:
Vrms = Vpk / sqrt(2)
90 = Vpk / sqrt(2)
Vpk = 90 * sqrt(2) ≈ 127.28 volts
Now, we can calculate the peak current:
Ipk = Vpk / Z
Ipk = 127.28 / 120 ≈ 1.06 A
Finally, we can use the formula P = I^2 * R to find the maximum power consumed by the circuit:
P = Ipk^2 * R
P = (1.06)^2 * 64
P ≈ 72.58 watts
Therefore, the maximum power delivered to the series RLC circuit when Vrms is 90 volts is approximately 72.58 watts.