Power in AC Circuits

A series LCR circuit is made by taking $R=100\mathrm{\Omega },L=\frac{2}{\pi }\mathrm{H},C=\frac{100}{\pi }\mathrm{\mu F}$ . This series combination is connected across an a.c. source of $220 \mathrm{V}, 50 \mathrm{Hz}$. Calculate (i) the impedance of the circuit and
(ii) the peak value of the current flowing in the circuit.
(iii) Calculate the power factor of this circuit.

The instantaneous current and voltage of an AC circuit are given by $\mathrm{i}=10\sin \left(314\mathrm{t}\right) \mathrm{A}$ and $\mathrm{V}=100\sin \left(314\mathrm{t}\right) \mathrm{V}$. What is the power dissipation in the circuit?

. The voltage difference between two terminals of an AC circuit is$V=5\cos \left(2\pi ft\right) \mathrm{V}$, the current flows in the circuit is $I=2\sin (2\pi ft) \mathrm{A}.$ Then the rate of energy loss in the circuit is

Given below are two statements:

Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.

Statement II: An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer from the options given below:

A series LCR circuit is connected across a source of emf $E=20 \sin (50\pi t- \frac{\pi }{3}) \mathrm{V}$. If a current $I=10\sin \left(50\pi t\right)$ $\mathrm{A}$flows in the circuit, then the power dissipated through circuit is ($t$ is in $s$)

Statement $\left(1\right):$ An LCR circuit connected to an AC source has maximum average power at resonance.

Statement $\left(2\right):$ A resistor only circuit with zero phase difference has maximum average power.

 A series LCR circuit with $R=20 \mathrm{\Omega }$, $L=2 \mathrm{H}$ and $C=50 \mu \mathrm{F}$ is connected to $200$ $ac$ source of variable frequency. What is (i) the amplitude of the current, and (ii) the average power transferred to the circuit in one complete cycle, at resonance ? (iii) Calculate the potential drop across the capacitor.

Which of the ac circuits with the following input voltage and current dissipates maximum power $P$?

In series LCR circuit shown in the figure, the current and potential difference across elements is given, the average power dissipated in circuit is

For a series LCR circuit, at resonance frequency$\left({\omega }_0\right)$, inductive reactance ${\omega }_{0}L=\frac{2}{\sqrt{3}}R$ and $P_0$ is the
 power dissipated across the circuit. If now operating frequency is increased to $\omega =2{\omega }_0$ and $P$ is the power dissipation across the circuit, then find the ratio $\frac{P}{P_0}$.

The phase difference between current and ac source voltage is $53°$. If rms value of current and voltage is $10 \mathrm{A}$ and $20 \mathrm{V}$ respectively, then power dissipated in the circuit is

An alternating current is represented by $i = 70.7 \sin 520 t$. Determine :

1. Frequency

2.  The current at $0.0015 \mathrm{s}$ after passing through zero increasing positively
3. r.m.s. value
4. Average value.

Identify the incorrect statement with respect to power ractor.

The current '$i$' in a circuit containing resistance $R=10\Omega$ and inductive reactance $X_L=7.5\Omega$ varies with time '$t$' as shown in the figure. The average power consumed in the circuit is

In a series $\mathrm{LCR}$ circuit, the inductive reactance $X_L=4\mathrm{\Omega }$, the capacitive reactance $X_C=10\mathrm{\Omega }$ and the resistance $R=6\mathrm{\Omega }$. The power factor of the circuit is

The power factor of LCR circuit which is in a state of resonance is

A circuit consists of a resistance of $6\Omega ,$ a capacitance of $2\mu \mathrm{F}$ and an inductance of $0.01\mathrm{H},$ in series with a power supply of $12\sin \left(\omega t\right)$ (Volts). Internal resistance of rest of the circuit is negligible. If the frequency of the power supply is such that the circuit is in resonance, average power generated by the power supply is

Power dissipated in an $\mathrm{LCR}$ series circuit connected to an $AC$ source of EMF $E$ is

In an $AC$ circuit, which has unknown electrical devices connected in series having resistance $3 \Omega$, the power factor is $\frac{3}{5}$. The resistance of circuit is