A circuit connected to an ac source of emf e = e 0 sin ⁡ 100 t with t in seconds, gives a phase difference of π 4 between the emf e and current i . Which of the following circuits will exhibit this?

R C circuit with R = 1 k Ω and C = 10 μ F

R C circuit with R = 1 k Ω and C = 1 μ F

R L circuit with R = 1 k Ω and L = 1 m H

R L circuit with R = 1 k Ω and L = 10 m H

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A unit step voltage is applied at t = 0 to a series R-L circuit with zero initial conditions

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Important Questions on Transient Current and Alternating Current

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

A sinusoidal voltage of peak value

283 V

and angular frequency

320 s^{- 1}

is applied to a series

L C R

circuit. Given that

R = 5 Ω, L = 25 mH

and

C = 1000 μF

. The total impedance and phase difference between the voltage across the source and the current will respectively be-

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

When the rms voltages

V_{L}, V_{C}

and

V_{R}

are measured respectively across the inductor

L,

the capacitor

C

and the resistor

R

in a series

L C R

circuit connected to an

A C

source, it is found that the ratio

V_{L} : V_{C} : V_{R} = 1 : 2 : 3.

If the rms voltage of the

A C

source is

100 V,

then

V_{R}

is close to :

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

A series R-C circuit is connected to an alternating voltage source. Consider two situations:

i. When capacitor is air filled.

ii. When capacitor is mica filled.

Current through resistor is

i

and voltage across capacitor is

V

then:

MEDIUM

Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

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:

MEDIUM

Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

A circuit connected to an ac source of emf

e = e_{0} \sin (100 t)

with

t

in seconds, gives a phase difference of

\frac{π}{4}

between the emf

e

and current

i

. Which of the following circuits will exhibit this?

HARD

Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

An AC voltmeter connected between points $A$ and $B$ in the circuit below reads $36 V .$ If it is connected between $A$ and $C,$ the reading is $39 V .$ The reading when it is connected between $B$ and $D$ is $25 V$ . What will the voltmeter read when it is connected between $A$ and $D ?$ ( Assume that the voltmeter reads true RMS voltage values and that the source generated a pure AC.)

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

Choose the wrong statement for the pure inductive circuit.

HARD

Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

If the input voltage $V_{i}$ to the circuit below is given by $V_{i} (t) = A \cos (2 π f t),$ the output voltage is given by $V_{o} (t) = B \cos (2 π f t + ϕ)$ .

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Which one of the following four graphs best depict the variation of $ϕ$ vs $f$ ?

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

Out of the following graphs, which graph shows the correct relation (graphical representation) for LC Parallel resonant circuit?

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

A small signal voltage

V (t) = V_{0} \sin ω t

is applied across an ideal capacitor

C

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

A bird sitting on a single high tension wire does not get electrocuted because

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

An alternating voltage

V (t) = 220 \sin (100 π t)

volt is applied to a purely resistive load of

50 Ω

. The time taken for the current to rise from half of the peak value to the peak value is:

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

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})

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

An inductor of inductance

L

and resistor

R

are joined together in series and connected by a source of frequency

ω

. The power dissipated in the circuit is

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

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

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

750 Hz, 20 V (rms)

source is connected to a resistance of

100 Ω,

an inductance of

0.1803 H

and a capacitance of

10 μ F

all in series. The time in which the resistance (heat capacity

2 J / ° C

) will get heated by

10 ° C .

(assume no loss of heat to the surroundings) is close to :

HARD

Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

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

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

An alternating voltage

V = V_{0} s i n ω t

is connected to a capacitor of capacity

C

through an A.C. ammeter of zero resistance. The reading of ammeter is

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Physics>Electricity and Magnetism>Transient Current and Alternating Current>Phasor Diagram in AC

For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor

C^{'}

, when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor

C^{'}

, must have been connected in:
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A unit step voltage is applied at t = 0 to a series R-L circuit with zero initial conditions

Important Questions on Transient Current and Alternating Current

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