A series LCR circuit with R = 20 W, L = 1.5 H and C = 35 μF is connectedto a variable-frequency 200 V ac supply. When the frequency of thesupply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
Given: The values of resistance is 20 Ω , inductance is 1 .5 H , capacitor is 35 μ F and the supply voltage is 200 V .
The impedance of the circuit is given as,
Z = ( R ) 2 + ( X L − X C ) 2
Where, the resistance is R , inductive reactance is X L and capacitive reactance is X C .
When the frequency of supply equals the natural frequency of the circuit, the circuit behaves as a purely resistive circuit. Hence,
Z = R
By substituting the values in the above equation, we get
Z = 20 Ω
The current in the circuit can be calculated as,
I = V Z
Where, the supply voltage is V and the impedance is Z .
By substituting the values in the above equation, we get
I = 200 20 = 10 A
The average power transferred to the circuit in one complete cycle is given as,
P = V I
By substituting the values in the above equation, we get
P = 200 × 10 = 2000 W
Thus, power transferred to the circuit in one complete cycle is 2000 W .
Given: The values of resistance is
The impedance of the circuit is given as,
Where, the resistance is
When the frequency of supply equals the natural frequency of the circuit, the circuit behaves as a purely resistive circuit. Hence,
By substituting the values in the above equation, we get
The current in the circuit can be calculated as,
Where, the supply voltage is
By substituting the values in the above equation, we get
The average power transferred to the circuit in one complete cycle is given as,
By substituting the values in the above equation, we get
Thus, power transferred to the circuit in one complete cycle is
