What is the average power dissipation in “L” in an RLC series circuit with R = 10ohm, L = 0.1 H, C = 10 microF when driven by a 100 V-rms source?
Wouldn't it depend on frequency?
The power dissipated is I^2*R
where I= 100Volts/ Z where Z is the resultant imedance.
Correction: Z = R = 10 ohms.
P = 100^2/10 = 1000 W.
To find the average power dissipation in the inductor (L) in an RLC series circuit, we can follow these steps:
Step 1: Calculate the impedance of the circuit (Z):
The impedance (Z) can be calculated using the formula: Z = √[(R^2) + ((ωL - 1/(ωC))^2)]
Here, R is the resistance, ω is the angular frequency (ω = 2πf), L is the inductance, and C is the capacitance.
Given: R = 10 ohm, L = 0.1 H, C = 10 microF = 10 × 10^(-6) F, f = frequency = 1/(2π√(LC)) = 1/(2π√(0.1 × 10^(-6) × 10 × 10^(-6)))
Now, substitute the given values into the formula to find Z.
Step 2: Calculate the current (I):
The current flowing in the circuit can be calculated using Ohm's Law: I = V/Z
Here, V is the rms voltage of the source.
Step 3: Calculate the average power dissipation in the inductor (P):
The average power dissipation in the inductor (L) can be calculated using the formula: P = (I^2) × Re(L), where Re(L) is the real component of the inductor impedance.
Let's calculate the average power dissipation in the inductor in the RLC series circuit:
Step 1: Calculate the impedance (Z):
Using the given values, substitute R = 10 ohm, L = 0.1 H, C = 10 × 10^(-6) F, and calculate Z using the formula.
Step 2: Calculate the current (I):
Using the given value of the rms voltage V = 100 V and the impedance Z calculated in step 1, substitute them into Ohm's Law to find I.
Step 3: Calculate the average power dissipation (P):
Using the calculated value of current (I) from step 2 and the real component of the inductor impedance (Re(L)), calculate P using the formula.
By following these steps, you should be able to calculate the average power dissipation in the inductor (L) in the RLC series circuit.
At the resonant frequency:
Xl = -Xc
Xl+Xc = 0.
Therefore, Z = R = 116 ohms.
P = E^2/R = 100^2/116 = 86.2 W.