A series LCR circuit with R = 1 kΩ , L = 1 . 0 mH , C = 0 . 001 μF is connected to a sinusoidal voltage of peak value 200 2 V . When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one cycle.

frequency of supply = natural frequency Resonance impedance (z) = R . 1 kΩ = 1000 Ω ∴ v 0 = 200 2 = v rim = v 0 2 = 200 V I rims = V rims z = 200 1000 = 0 . 2 A ∴ pavg = v rims . I rims . cosϕ for resonance , ϕ = 0 Pavg = 200 × 0 . 2 × 1 = 40 W

Show that the total energy of LC circuit in V = V E 1 2 q m 2 C .

Image result for Show that the total energy of LC circuit in V=VE12q2mC. UL=12LI20. Since there is no resistance in the circuit, no energy is lost through Joule heating; thus, the maximum energy stored in the capacitor is equal to the maximum energy stored at a later time in the inductor: 12q20C=12LI20. q2(t)2C+Li22.An LC circuit. in Equation (40) is the total energy of the circuit, and that this energy is a conserved quantity. The oscillations of an LC circuit can, thus, be understood as a cyclic interchange between electric energy stored in the capacitor, and magnetic energy stored in the inductor.

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Is an oscillating LC circuit the maximum charge?

Important Questions on AC Circuits

HARD

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to

Q_{0}

and then connected to the L and R as shown below:
Question Image

If a student plots graphs of the square of maximum charge

(Q_{M a x}^{2})

on the capacitor with time (t) for two different values

L_{1}

and

L_{2} (L_{1} > L_{2})

of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)

EASY

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

L C

oscillations are similar and analogous to the mechanical oscillations of a block attached to a spring. The electrical equivalent of the force constant of the spring is

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

Define quality factor?

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

A series LCR circuit with

R = 1 kΩ, L = 1.0 mH, C = 0.001 μF

is connected to a sinusoidal voltage of peak value

200 \sqrt{2} V

. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one cycle.

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

A fully charged capacitor

C

with initial charge

q_{0}

is connected to a coil of self-inductance

L

t = 0 .

The time at which the energy is stored equally between the electric and the magnetic fields is:

EASY

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

How does the

L - C

circuit produce oscillation? Explain.

EASY

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

If the instantaneous emf and the instantaneous current equations of an A.C. circuit are respectively.

$e = E 0 \sin (ω t - π / 6), i = I 0 \sin (ω t + π / 6),$ then the phase difference between voltage and current is :

HARD

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

Using the equation

$\frac{di}{dt} + \frac{R}{L} i + \frac{1}{LC} \int idt = \frac{V_{m}}{L} e^{iωt}$ . for L-C-R circuit, obtain an equation for the complex current $' i'$ and explain its different terms in the equation. Hence obtain the equation for real current $' i'$

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

At a certain moment, the switch shown in the figure is disconnected. The energy of the oscillations immediately after the switch $S$ is disconnected and at time $0.1 \sec$ from the time switch is disconnected are, respectively

Question Image

HARD

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

In an LC circuit connected to an ac supply, the resonant frequency is

200 MHz

when a dielectric of thickness

8 mm

and dielectric constant

6

is fully inserted between the plates of the capacitor. The resonant frequency becomes

198 MHz

when a stress of

995

bar is applied between the plates of the capacitor. The Young's modulus of the dielectric material in

{Nm}^{- 2}

is nearly

EASY

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

Show that the total energy of LC circuit in

V = V_{E} \frac{1}{2} \frac{q_{m}^{2}}{C}

HARD

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

L C R

circuit behaves like a clamped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant

' b^{'},

the correct equivalence would be:

EASY

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

The frequency of output signal becomes_______ times by increasing the value of capacitance

4

times the original in LC oscillation circuit

HARD

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

Obtain an expression for the energy associated with an inductor.

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

In an L-C Oscillatory circuit having a completely charged capacitor, with passage of time_______

EASY

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

What is the phase difference between the input and the output voltage in a transistor oscillator circuit?

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

In an L-C oscillator circuit having a completely charged capacitor, with the passage of time _____.

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

In an oscillating

L C

circuit,

L = 3.00 mH

and

C = 2.70 μ F

. At

t = 0

the charge on the capacitor is zero and the current is

2.00 A

. The maximum charge that will appear on the capacitor will be

HARD

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

L C

circuit the inductance

L = 40 mH

and capacitance

C = 100 μF .

If a voltage

V (t) = 10 s i n (314 t)

is applied to the circuit, the current in the circuit is given as:

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>LC Oscillations

An oscillator circuit contains an inductor

0.05 H

and a capacitor of capacity

80 μF

. When the maximum voltage across the capacitor is

200 V

, the maximum current (in amperes) in the circuit is

Is an oscillating LC circuit the maximum charge?

Important Questions on AC Circuits

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