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 potential difference $V$and the current $I$ flowing through an A.C circuit is given by $V=5 \cos (\omega t-\frac{\mathrm{\pi }}{6})$ in volt  and $I=10 \sin \left(\omega t\right)$ in ampere. The average power dissipated in the circuit is:

An alternating voltage of $260 \mathrm{V}$ and $\omega =100 \mathrm{rad} {\mathrm{s}}^{-1}$ is applied across an $LCR$ series circuit, where $L=0.01 \mathrm{H}, C=4\times {10}^{-4} \mathrm{F}$ and $R=10 \mathrm{\Omega }$. Find the inductive reactance and the power supplied by the source:

The potential difference $V$and the current $I$ flowing through an A.C circuit is given by $V=5 \cos (\omega t-\frac{\mathrm{\pi }}{6})$ volt and $I=10 \sin \omega t$ ampere. The average power dissipated in the circuit is:

A circuit has an inductor of inductance $5 \mathrm{H}$ and a resistor of resistance $2500 \mathrm{\Omega }$ at a frequency of $500 \mathrm{rad}/\mathrm{s}$? What is the ratio of the real power to the reactive power?

The power factor of a coil is $0.707$ at frequency $50 \mathrm{Hz}$. If frequency is doubled, say the power factor of coil becomes $\frac{1}{\sqrt{n}}$. What is $n$?

In a series resonant circuit, having $\mathrm{L}, \mathrm{C}$ and $\mathrm{R}$as its elements, the resonant current is $i$. The power dissipated in the circuit at resonance is

A resitance '$R$' draws power '$P$' when connected to an $AC$ source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes '$Z$', the power drawn will be:

A coil has a resistance $10 \mathrm{\Omega }$ and an inductance of $0.4$ Henry. It is connected to an $\mathrm{AC}$ source of $6.5 V, \frac{30}{\pi }\mathrm{Hz}.$ The average power consumed in the circuit, is :-

The voltage $\text{V}$ and current $\text{i}$ in AC circuit are given by,

$V=50 \sin \left(50t\right) \mathrm{volt}$

$i=50 \sin \left(50t+\frac{\pi }{3}\right) \mathrm{mA}$

The power dissipated in circuit is:

The potential difference $V$and the current $I$ flowing through an A.C circuit is given by $V=5 \cos (\omega t-\frac{\mathrm{\pi }}{6})$ volts and $I=10 \sin \left(\omega t\right)$ amperes. The average power dissipated in the circuit is:

The power dissipated in the adjacent circuit is-

In an ac circuit the voltage and current are $V\mathit{=}{V}_{m}sin\mathit{ }\omega t$ and $I\mathit{=}{I}_{m}sin\mathit{ }\left(\omega t\mathit{-}\frac{\pi }{\mathit{2}}\right)$, the power dissipated in the circuit will be-

In a particular series $\mathrm{LR}$ circuit, it is known that the voltage drop across inductor iand resistor is $8 \mathrm{V}$ and $6 \mathrm{V}$ respectively. Calculate the voltage supplied and the power factor of the circuit.

Calculate the power factor of an  circuit that has a resistance of $12 \mathrm{\Omega }$ and an impedence of $15 \mathrm{\Omega }$ in series.

For a particular series $\mathrm{LR}$ circuit, the inductive reactance is  $X_L=3R$. Now in the circuit a capacitor with reactance $X_C=R$ is also added in series. What is the ratio of new to old power factor?

In a particular $\mathrm{LR}$ circuit, the series combination of resistance $R$ and inductance $L$ is connected to an alternating source of EMF $e=311\sin \left(100\mathrm{\pi }t\right)$. Calculate the power factor of the circuit, if it is known that the value of wattless current is $0.5 \mathrm{A}$ and the impedance of the circuit is $311 \mathrm{\Omega }$.

Calculate the power dissipated in the LCR circuit with $R=100 \mathrm{\Omega }$ and on taking out the capacitance from the circuit, the current lags behind the voltages by $60°$ while it leads by the same when only inductor is taken out of the circuit. The rms value and angular frequency of the voltage supply is  $200 \mathrm{V}$ and $300 \mathrm{rad} {\mathrm{s}}^{-1}$ respectively.

What is the average power consumed by a circuit with voltage $V_S=200\sqrt{2}\sin (\omega t+15°)$ and current $i=2\sin (𝝎t+\mathrm{\pi }/4)$.