At resonance, the frequency of the supply power equalsthe natural frequency of the given LCR circuit.
Resistance, R = 20 Ω Inductance, L = 1.5 H Capacitance, C = 35 µF = 30 × 10−6 F
AC supply voltage to the LCR circuit, V = 200 V
Impedance of the circuit is given by the relation,
\(Z=√(R^2+(X_L-X_C))^2 At resonance, X_L=X_C\)
Z=R=20Ω
Current in the circuit can be calculated as:
\(I=\frac{V}{Z}=\frac{200}{20}=10 A\)
Hence, the average power transferred to the circuit in one complete cycle:
VI = 200 × 10 = 2000 W.
At resonance, the frequency of supply power equals to naturan frequency of LCR circuit.
Impedence,
\(Z = \sqrt {R^2 + (ω_L - \frac {1}{ω_C})}\)
\(ω_L=\frac {1}{ ωc}\)
So, \(Z = R\)
Current \(I = \frac VR\)
\(I= \frac {200}{20}\)
\(I= 10\ A\)
Power,
\(P =VI\)
\(P= 200 \times 10\)
\(P= 2000\ W\)
So, the answer is 2000 W.
An LCR circuit, also known as a resonant circuit, or an RLC circuit, is an electrical circuit consist of an inductor (L), capacitor (C) and resistor (R) connected in series or parallel.
When a constant voltage source is connected across a resistor a current is induced in it. This current has a unique direction and flows from the negative to positive terminal. Magnitude of current remains constant.
Alternating current is the current if the direction of current through this resistor changes periodically. An AC generator or AC dynamo can be used as AC voltage source.