Alternating current practice · Mixed difficulty

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:

What will be the self inductance of a coil, to be connected in a series with a resistance of $\pi \sqrt 3 \mathrm{\Omega }$ such that the phase difference between the emf and the current at 50 Hz frequency is 30°

In an ideal transformer the number of turns of primary and secondary coil is given as $\mathrm{100}$ and $\mathrm{300}$ respectively. If the power input is $60\,\,W$, the power output is

In a current I given by ${I_\mathrm{o}}\sin \left[ {\omega t - \frac{\pi }{2}} \right]$ flows in an AC circuit across which an AC potential of $E = {E_\mathrm{o}}$ sin wt has been applied, then the power consumption $P$ in the circuit will be

The hysteresis cycle for the material of a transformer core is

Power factor of an L-R series circuit is 0.6 and that of a C-R series circuit is 0.5 . If the elements ( $L, C$ and $R$ ) of the two circuit are joined in series the power factor of this circuit is found to be 1. The ratio of the resistance is L-R circuit to the resistance in the C-R circuit is

Choose the incorrect statement

In an AC circuit, V and I are given by $V = 150\sin \left( {150\mathrm{t}} \right)\mathrm{\;volt\;and\;}I = 150\sin \left( {150\mathrm{t} + \frac{\mathrm{\pi }}{3}} \right)\mathrm{amp}$ . The power dissipated in the circuit is

A bulb is connected first with dc and then ac of same voltage it will shine brightly with

A pure inductive coil of 30 mH is connected to an AC source of 220 V, 50 Hz. The rms current in the coil is

A transformer with turns ratio $\frac{N_1}{N_2}=\frac{50}{1}$ is connected to a 120 volt AC supply. If primary and secondary circuit resistance are $1.5 \mathrm{~k} \Omega$ and $1 ~\Omega$ respectively then find out power output.

An electric heater rated 220 V and 550 W is connected to A.C mains. The current drown by it is

Which of the following components of a L – C – R circuit, with AC supply, dissipates energy?

The primary winding of a transformer has 200 turns and its secondary winding has 50 turns. If the current in the secondary winding is 40 A, the current in the primary is

The values of L, C and R for a circuit are 1H, 9F and 3Ω. What is the quality factor for the circuit at resonance?

If $L,C$ and $R$ are the self-inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

If the direction of i is reversed, $\left( {{V_B} - {V_A}} \right)$ will be

The instantaneous values of current and emf in an ac circuit are $I = 1/\sqrt 2$ $\sin 314\;t\;amp$ and $E = \sqrt 2 \sin \left( {314\;t - \pi /6} \right)V$ respectively. The phase difference between E and I will be

In a series L-C-R circuit R=200 Ω and the voltage and the frequency of the main supply is 220V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30°. On taking out the inductor from the circuit the current leads the voltage by 30°. The power dissipated in the L-C-R circuit is

A series $L-C-R$ circuit is connected to an $\mathrm{AC}$ voltage source. When $L$ is removed from the circuit, the phase difference between current and voltage is $\frac{\pi}{4}$. If instead $C$ is removed from the circuit, the phase difference is again $\frac{\pi}{4}$ between current and voltage. The power factor of the circuit is

An L – C – R circuit of R=100 Ω is connected to an AC source 100 V, 50 Hz. The magnitude of phase difference between current and voltage is 30°. The power dissipated in the L – C – R circuit is

An AC circuit consists of a $220 \Omega$ resistance and a $0.7 \mathrm{H}$ choke. The power absorbed from $220 \mathrm{~V}$ and $50 \mathrm{~Hz}$ source connected in this circuit, if the resistance and choke are joined in series is

A mixer of $100\,\,{\mkern 1mu} \Omega$ resistance is connected to an A.C. source of 200 v and 50 cycles/sec. The value of average potential difference across the mixer will be

A transformer of frequency $60 \mathrm{~Hz}$ and $120 \mathrm{~V}$ input has $8: 1$ turn ratio. The frequency of the output is

The ratio of turns in primary and secondary coils of a transformer is 1 : 20. The ratio of currents in primary and secondary coils will be

Assertion: A bulb connected in series with a solenoid is connected to ac source. If a soft iron core is introduced in the solenoid, the bulb will glow brighter.

Reason: On introducing soft iron core in the solenoid, the inductance increases.

In a uniform magnetic field of induction B a wire in the form of a semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $\mathrm{R}$, the mean power generated per period of rotation is :

A series LCR circuit with $R=20^{\prime} \Omega, L=1.5 \mathrm{H}$ and $\mathrm{C}=35$ $\mu \mathrm{F}$ is connected to a variable-frequency $200 \mathrm{~V}$ ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power in $\mathrm{Kw}$ transferred to the circuit in one complete cycle?

Assertion: The alternating current lags behind the e.m.f. by a phase angle of $\pi / 2$, when ac flows through an inductor.

Reason: The inductive reactance increases as the frequency of ac source decreases.

A pure resistive circuit element $X$ when connected to an AC supply of peak voltage $200 \mathrm{~V}$ gives a peak current of $5 \mathrm{~A}$ which is in phase with the voltage. A second circuit element $\mathrm{Y}$, when connected to the same AC supply also gives the same value of peak current but the current lags behind by $90^{\circ}$. If the series combination of $\mathrm{X}$ and $\mathrm{Y}$ is connected to the same supply, the rms valus of current is