Deduce an equation U = 1 2 LI 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power , rate of doing work) = ε I dt ( power = voltage (emf) x current ) But ε = - L di dt ( in case of an inductor) therefor dw = L dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

Deduce an equation U = 1 2 L I 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power, rate of doing work ). = ε I dt (power = voltage (emf) x current). But ε = - L di dt (in case of an inductor). therefor dw = LI dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

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In a pure inductive circuit negative and positive loop under power curve is the same.

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Important Questions on Alternating Current

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

A pure inductor of,

30.0 mH

is connected to a source of,

250 V

. Find the inductive reactance (in

Ω

) and R.M.S. current (in

A

) in the circuit if the frequency of the source is

80 Hz

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

Which of the following represents the variation of inductive reactance

(X_{L})

with the frequency of voltage source

(ν) ?

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

For a given frequency, the inductive reactance of a coil at

100 H

25 Ω

. For the same frequency, the inductance reactance at

200 H

will be

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

What is the principle of choke coil? Why is the current in the choke coil called wattless current? Write its application in current control.

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

Choose the wrong statement for the pure inductive circuit.

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

An applied

e . m . f .

signal consists of superposition of a d.c. source and a.c. source of high frequency. The circuit consists of an inductor

L

and a capacitor

C

in series. Show that d.c. signal appears across

C

and a.c. signal appears across

L

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

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

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

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 becomes zero.
In the light of the above statements, choose the correct answer from the options given below

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

An inductance coil has a reactance of

100 Ω

. When an AC signal of frequency

1000 Hz

is applied to the coil, the applied voltage leads the current by

45 °

. The self-inductance of the coil is

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

Three identical emf sources are attached to a single circuit element: a resistor, a capacitor, or an inductor. The current amplitude is then measured as a function of frequency. Which one of the following curve corresponds to inductive circuit?

Question Image

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

Deduce an equation

U = \frac{1}{2} {LI}^{2}

for an inductor.

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

A voltage

V_{PQ} = V_{0} \cos (ωt)

(where,

V_{0}

is a real amplitude) is applied between the points

P

and

Q

in the network shown in the figure. The values of capacitance and inductance are

C = \frac{1}{ω R \sqrt{3}}

and

L = \frac{R \sqrt{3}}{ω}

. Then, the total impedance between

P

and

Q

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

Deduce an equation

U = \frac{1}{2} L I^{2}

for an inductor.

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

The phase difference between current and voltage in an A.C. circuit containing inductance only is.

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

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 $\frac{\sqrt{a}}{π} A$ . The value of $a$ is _____ .

Question Image

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

A coil of inductance

0.1 H

and resistance

110 Ω

is connected to a source of

110 V

and

350 Hz

. The phase difference between the voltage maximum and the current maximum is

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

The equation of current in a purely inductive circuit is

5 \sin (49 π t - 30 °)

. If the inductance is

30 mH

then the equation for the voltage across the inductor, will be

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

600 Hz

, an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at

60 Hz

will be

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

A series

L R

circuit is connected to a voltage source with

V (t) = V_{0} \sin (ω t)

. After a very large time, current

I (t)

behaves as

(t_{0} ≫ \frac{L}{R})

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Inductor

A resistance

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:

In a pure inductive circuit negative and positive loop under power curve is the same.

Important Questions on Alternating Current

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