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.

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

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In an L-C oscillation maximum charge on capacitor can be $Q_{0}$ . If at any instant electrical energy is $\frac{3}{4}$ th of the magnetic energy then the charge on capacitor at that instant is

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Important Questions on Alternating Current

EASY

Physics>Electricity and Magnetism>Alternating Current>LC Oscillations

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

4

times the original in LC oscillation circuit

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>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

EASY

Physics>Electricity and Magnetism>Alternating Current>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 :

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>LC Oscillations

Define quality factor?

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>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>Alternating Current>LC Oscillations

A radio receiver can tune over the frequency range

300 kHz

1200 kHz

. If the tunable

L C

circuit has a fixed inductor

L = 200 μ H

, what must be the range over which the capacitor must be tuned? (You can use

π^{2} \approx 10

)

EASY

Physics>Electricity and Magnetism>Alternating Current>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

EASY

Physics>Electricity and Magnetism>Alternating Current>LC Oscillations

Show that the total energy of LC circuit in

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

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>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>Alternating Current>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

HARD

Physics>Electricity and Magnetism>Alternating Current>LC Oscillations

Obtain an expression for the energy associated with an inductor.

HARD

Physics>Electricity and Magnetism>Alternating Current>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>Alternating Current>LC Oscillations

How does the

L - C

circuit produce oscillation? Explain.

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>LC Oscillations

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

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>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>Alternating Current>LC Oscillations

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

HARD

Physics>Electricity and Magnetism>Alternating Current>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>Alternating Current>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>Alternating Current>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:

HARD

Physics>Electricity and Magnetism>Alternating Current>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)

In an L-C oscillation maximum charge on capacitor can be Q0. If at any instant electrical energy is 34th of the magnetic energy then the charge on capacitor at that instant is

Important Questions on Alternating Current

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In an L-C oscillation maximum charge on capacitor can be $Q_{0}$ . If at any instant electrical energy is $\frac{3}{4}$ th of the magnetic energy then the charge on capacitor at that instant is