Alternating Current

To increase the resonant frequency in series LCR circuit,

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on :

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is \({{\sqrt a } \over \pi }\) A. The value...

A resistance of 40 \(\Omega\) is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value :

Given below are two statements :
Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement II : In ac circuit, the average power delivered by the source never becom...

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with XL = R = XC. Impedance of this circuit is :

At very high frequencies, the effective impendence of the given circuit will be ________________ \(\Omega\).

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then T1 is connected to T2. As the current in R = 6\(\Omega\) attains a maximum value of steady state level, T1 is disconnected from T2 and immediately ...

A 0.07 H inductor and a 12\(\Omega\) resistor are connected in series to a 220V, 50 Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take \(\pi\) as $${{22} \over...

A 100\(\Omega\) resistance, a 0.1 \(\mu\)F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant f...

The alternating current is given by \(i = \left\{ {\sqrt {42} \sin \left( {{{2\pi } \over T}t} \right) + 10} \right\}A\)The r.m.s. value of of this current is ................. A.

An ac circuit has an inductor and a resistor resistance R in series, such that XL = 3R. Now, a capacitor is added in series such that XC = 2R. The ratio of new power factor with the old power factor of the circuit is \(\sqrt 5 :x\). The val...

An alternating current is given by the equation i = i1 sin \(\omega\)t + i2 cos \(\omega\)t. The rms current will be :

In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.

Find the peak current and resonant frequency of the following circuit (as shown in figure).

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 k\(\Omega\), an inductor of inductive reactance XL = 250 \(\pi\)\(\Omega\) and an unknown capacitor. The value of capacitance to maximize the average p...

In the given circuit the AC source has \(\omega\) = 100 rad s-1. Considering the inductor and capacitor to be ideal, what will be the current I flowing through the circuit?

An inductor of 10 mH is connected to a 20V battery through a resistor of 10 k\(\Omega\) and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after 1 \(\mu\)s...

Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the average power dissipated in one cycle will be same in both the circuits.

A 10 \(\Omega\) resistance is connected across 220V \(-\) 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is :

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 \(\mu\)F is used in the resonant circuit. The self inductance of coil necessary for resonance is __________ \(\times\) 10\(-\)8 H.

The current (i) at time t = 0 and t = \(\infty\) respectively for the given circuit is :

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

An LCR circuit contains resistance of 110\(\Omega\) and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45\(^\circ\). If on the other hand, only inductor ...

Match List I with List II.



List I

List II




(a)
Rectifier
(i)
Used either for stepping up or stepping down the a.c. voltage


(b)
Stabilizer
(ii)
Used to convert a.c. voltage i...

A resonance circuit having inductance and resistance 2 \(\times\) 10\(-\)4 H and 6.28\(\Omega\) respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is ___________. [\(\pi\) = 3.14]

A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C.) on standard domestic A.C. supply. The number of turns of...

A series L-C-R circuit is designed to resonate at an angular frequency \(\omega\)0 = 105 rad/s. The circuit draws 16W power from 120V source at resonance. The value of resistance 'R' in the circuit is _________ \(\Omega\).

Match List - I with List - II



List - I

List - II




(a)
\(\omega L > {1 \over {\omega C}}\)
(i)
Current is in phase with emf


(b)
\(\omega L = {1 \over {\omega C}}\)
(ii)
Curre...

In a circuit consisting of a capacitance and a generator with alternating emf Eg = Eg0 sin\(\omega\)t, VC and IC are the voltage and current. Correct phasor diagram for such circuit is

In an LCR series circuit, an inductor 30 mH and a resistor 1 \(\Omega\) are connected to an AC source of angular frequency 300 rad/s. The value of capacitance for which, the current leads the voltage by 45\(^\circ\) is $${1 \over x} \times ...

AC voltage V(t) = 20 sin\(\omega\)t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m2. The amplitude of the oscillating displacement current for the applied AC voltag...

A series LCR circuit of R = 5\(\Omega\), L = 20 mH and C = 0.5 \(\mu\)F is connected across an AC supply of 250 V, having variable frequency. The power dissipated at resonance condition is ______________ \(\times\) 102 W.

For a series LCR circuit with R = 100 \(\Omega\), L = 0.5 mH and C = 0.1 pF connected across 220V\(-\)50 Hz AC supply, the phase angle between current and supplied voltage and the nature of the circuit is :

For the given circuit the current i through the battery when the key in closed and the steady state has been reached is __________.

An AC source rated 220 V, 50 Hz is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :

In a series LCR circuit, the inductive reactance (XL) is 10\(\Omega\) and the capacitive reactance (XC) is 4\(\Omega\). The resistance (R) in the circuit is 6\(\Omega\). The power factor of the circuit is :

An AC current is given by I = I1 sin\(\omega\)t + I2 cos\(\omega\)t. A hot wire ammeter will give a reading :

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

Match List - I with List - II



List - I

List - II




(a)
Phase difference between current and voltage in a purely resistive AC circuit
(i)
\({\pi \over 2}\); current leads voltage


(b)
...

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8\(\Omega\), L = 24 mH and C = 60 \(\mu\)F. The value of power dissipated at resonant condition is 'x' kW. The value of x to the nearest integer is __...

An RC circuit as shown in the figure is driven by a AC source generating a square wave. The output wave pattern monitored by CRO would look close to :

For the given circuit, comment on the type of transformer used.

In LC circuit the inductance L = 40 mH and
capacitance C = 100 \(\mu\)F. If a voltage
V(t) = 10sin(314t) is applied to the circuit, the
current in the circuit is given as :

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 \(\Omega\)
resistor. The ratio of the currents at time t = \(\infty\) and at t = 40 s is close to : (Take e2 = 7.389)

An AC circuit has R= 100 \(\Omega\), C = 2 \(\mu\)F and L = 80 mH, connected in series. The quality factor of the
circuit is :

In a series LR circuit, power of 400W is dissipated from a source of 250 V, 50 Hz. The power factor
of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in
series to the L and R. Taking the val...

A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then
the time at which the energy stored in the inductor reaches \(\left( {{1 \over n}} \right)\) times of its maximum value, is :