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question_answer1)
Directions : (1-5) |
LCR Circuit |
When a pure resistance R, pure inductor L and an ideal capacitor of capacitance C is connected in series to a source of alternating e.m.f., then current at any instant through the three elements has the same amplitude and is respresented as \[I={{I}_{0}}\]\[\sin \omega t\] at. However, voltage across each element has a different phase relationship with the current as shown in graph. |
The effective resistance of RLC circuit is called impedance (Z) of the circuit and the voltage leads the current by a phase angle \[\phi \]. |
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A resistor of \[12\,\Omega \], a capacitor of reactance \[14\,\Omega \] and a pure inductor of inductance 0.1 H are joined in series and placed across 200 V, 50 Hz. a. c. supply. |
The value of inductive reactance is
A)
\[15\,\Omega \] done
clear
B)
\[31\centerdot 4\,\Omega \] done
clear
C)
\[20\,\Omega \] done
clear
D)
\[30\,\Omega \] done
clear
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question_answer2)
The value of impedance is
A)
\[20\,\Omega \] done
clear
B)
\[15\,\Omega \] done
clear
C)
\[30\,\Omega \] done
clear
D)
\[21\centerdot 13\,\Omega \] done
clear
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question_answer3)
What is the value of current in the circuit?
A)
5 A done
clear
B)
15 A done
clear
C)
10 A done
clear
D)
\[9\centerdot 46\,A.\] done
clear
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question_answer4)
What is the value of the phase angle between current and voltage?
A)
done
clear
B)
\[63\text{ }{}^\circ 9'\] done
clear
C)
\[55\text{ }{}^\circ 4'\] done
clear
D)
\[50{}^\circ \] done
clear
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question_answer5)
From graph, which one is true from following?
A)
\[{{V}_{L}}\ge \,{{V}_{C}}\] done
clear
B)
\[{{V}_{C}}<\,{{V}_{C}}\] done
clear
C)
\[{{V}_{L}}>{{V}_{C}}\] done
clear
D)
\[{{V}_{L}}={{V}_{C}}\] done
clear
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question_answer6)
Directions : (6-10) |
AC Voltage Applied to a Capacitor |
Let a source of alternating e.m.f. \[E={{E}_{0}}\] \[\sin \omega t\] be connected to a capacitor of capacitance C. If 'I' is the instantaneous value of current in the circuit at instant t. then \[I=\frac{{{E}_{0}}}{I/\omega C}\,\sin \left( \omega t+\frac{\pi }{2} \right)\]. The capacitive reactance limits the amplitude of current in a purely capacitive circuit and it is given by \[{{X}_{C}}=\frac{1}{\omega C}\]. |
|
What is the unit of capacitive reactance?
A)
farad done
clear
B)
ampere done
clear
C)
ohm done
clear
D)
\[oh{{m}^{-1}}\] done
clear
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question_answer7)
The capacitive reactance of a \[5\mu F\]capacitor for a frequency of \[{{10}^{6}}\,Hz\] is
A)
\[0\centerdot 032\,\Omega \] done
clear
B)
\[2\centerdot 52\,\Omega \] done
clear
C)
\[1\centerdot 25\,\Omega \] done
clear
D)
\[4\centerdot 51\,\Omega \] done
clear
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question_answer8)
In a capacitive circuit, resistance to the flow of current is offered by
A)
resistor done
clear
B)
capacitor done
clear
C)
inductor done
clear
D)
frequency. done
clear
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question_answer9)
In a capacitive circuit, by what value of phase angle does alternating current leads the e.m.f. ?
A)
\[45{}^\circ \] done
clear
B)
\[90{}^\circ \] done
clear
C)
\[75{}^\circ \] done
clear
D)
\[60{}^\circ \] done
clear
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question_answer10)
One microfarad capacitor is joind to a 200 V, 50 Hz alternator. The rms current through capacitor is
A)
\[6\centerdot 28\times {{10}^{-2}}A\] done
clear
B)
\[7\centerdot 5\times {{10}^{-4}}A\] done
clear
C)
\[10\centerdot 52\times {{10}^{-2}}A\] done
clear
D)
\[15\centerdot 25\times {{10}^{-2}}A.\] done
clear
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question_answer11)
Directions : (11-15) |
AC Voltage Applied to an Inductor |
Let a source of alternating e.m.f. \[E={{E}_{0}}\,\sin \omega t\]be connected to a circuit containing a pure inductance L. If I is the value of instantaneous current in the ciruit, then \[I={{I}_{0}}\sin \left( \omega t-\frac{\pi }{2} \right)\]. The inductive reactance limits the current in a purely inductive circuit and is given by \[{{X}_{L}}=\omega L\]. |
|
A 100 hertz a. c. is flowing in a 14 mH coil. The reactance is
A)
\[15\,\Omega \] done
clear
B)
\[7\centerdot 5\Omega \] done
clear
C)
\[8\centerdot 8\Omega \] done
clear
D)
\[10\,\Omega \] done
clear
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question_answer12)
In a pure inductive circuit, resistance to the flow of current is offered by
A)
resistor done
clear
B)
inductor done
clear
C)
capacitor done
clear
D)
resistor and inductor done
clear
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question_answer13)
In a inductive circuit, by what value of phase angle does alternating current lags behind e.m.f.?
A)
\[45{}^\circ \] done
clear
B)
\[90{}^\circ \] done
clear
C)
\[120{}^\circ \] done
clear
D)
\[75{}^\circ \] done
clear
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question_answer14)
How much inductance should be connected to 200 V, 50 Hz a.c. supply so that a maximum current of \[0\centerdot 9A\] flows through it?
A)
5H done
clear
B)
1 H done
clear
C)
10 H done
clear
D)
\[4\centerdot 5H\] done
clear
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question_answer15)
The maximum value of current when inductance of 2 H is conneced to 150 volt, 50 Hz supply is
A)
\[0\centerdot 337A\] done
clear
B)
\[0\centerdot 721A\] done
clear
C)
\[1\centerdot 521A\] done
clear
D)
\[2\centerdot 522A\] done
clear
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question_answer16)
Directions : (16-20) |
Average Power Associated with an inductor and Capacitor |
The power averaged over one full cycle of a.c. is known as average power. It is also known as true power. |
\[{{P}_{av}}={{V}_{rms}}\,{{I}_{rms}}\cos \phi =\frac{{{V}_{0}}{{I}_{0}}}{2}\,\cos \phi \] |
Root mean square or simply rms watts refer to continuous power. |
A circuit containing a 80 mH inductor and a \[60\,\mu F\] capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible. |
|
The value of current amplitude is
A)
15 A done
clear
B)
\[11\centerdot 63A\] done
clear
C)
\[17\centerdot 65A\] done
clear
D)
\[6\centerdot 33A\] done
clear
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question_answer17)
Find rms value
A)
6 A done
clear
B)
\[5\centerdot 25A\] done
clear
C)
\[8\centerdot 23A\] done
clear
D)
\[7\centerdot 52A\] done
clear
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question_answer18)
The average power transferred to inductor is
A)
zero done
clear
B)
7 W done
clear
C)
\[2\centerdot 5W\] done
clear
D)
5 W done
clear
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question_answer19)
The average power transferred to the capacitor is
A)
5W done
clear
B)
zero done
clear
C)
11 W done
clear
D)
15 W done
clear
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question_answer20)
What is the total power absorbed by the circuit?
A)
Zero done
clear
B)
10 W done
clear
C)
\[2\,.\,5\,W\] done
clear
D)
15 W done
clear
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question_answer21)
Directions : (21-25) |
Case Study-5 |
A transformer is essentially an a.c. device. It cannot work on d.c. It changes alternating voltages or currents. |
It does not affect the frequency of a.c. It based on the phenomenon of mutual induction. A transformer essentially consists of two coils of insulated copper wire having different number of turns and wound on the same soft iron core. |
The number of turns in the primary and secondary coils of an ideal transformer are 2000 and 50 respectively. |
The primary coil is connected to a main supply of 120 V and secondary coil is connected to a bulb of resistance \[0\centerdot 6\Omega \]. |
The value of voltage across the secondary coil is
A)
5V done
clear
B)
2 V done
clear
C)
3V done
clear
D)
10 V done
clear
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question_answer22)
The value of current in the bulb is
A)
7 A done
clear
B)
15 A done
clear
C)
3 A done
clear
D)
5 A done
clear
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question_answer23)
The value of current in primary coil is
A)
\[0\centerdot 125A\] done
clear
B)
\[2\centerdot 52A\] done
clear
C)
\[1\centerdot 51A\] done
clear
D)
\[3\centerdot 52A\] done
clear
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question_answer24)
Power in primary coil is
A)
20 W done
clear
B)
5 W done
clear
C)
10 W done
clear
D)
15 W done
clear
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question_answer25)
Power in secondary coil is
A)
15 W done
clear
B)
20 W done
clear
C)
7 W done
clear
D)
8 W done
clear
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question_answer26)
Directions : (26-30) |
Resonant Series LCR Circuit |
When the frequency of ac supply is such that the inductive reactance and capacitive reactance become equal, the impedance of the series LCR circuit is equal to the ohmic resistance in the circuit. Such a series LCR circuit is known as resonant series LCR circuit and the frequency of the ac supply is known as resonant frequency. |
Resonance phenomenon is exhibited by a circuit only if both L and C are present in the circuit. We cannot have resonance in a RL or RC circuit. |
A series LCR circuit with \[L=0\centerdot 12\,H\], C = 480 nF, |
\[R=23\,\Omega \] is connected to a 230 V variable frequency supply. |
|
Find the value of source frequency for which current amplitude is maximum
A)
\[222\centerdot 32\,Hz\] done
clear
B)
\[550\centerdot 52\,Hz\] done
clear
C)
\[663\centerdot 48\,Hz\] done
clear
D)
770 Hz. done
clear
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question_answer27)
The value of maximum current is
A)
\[14\centerdot 14\,A\] done
clear
B)
\[22\centerdot 52\,A\] done
clear
C)
\[50\centerdot 25\,A\] done
clear
D)
\[47\centerdot 41\,A\] done
clear
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question_answer28)
The value of maximum power is
A)
2200 W done
clear
B)
\[2293\centerdot 3\,W\] done
clear
C)
5500 W done
clear
D)
4700 W done
clear
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question_answer29)
What is the Q-factor of the given circuit?
A)
25 done
clear
B)
\[42\centerdot 21\] done
clear
C)
\[35\centerdot 42\] done
clear
D)
\[21\centerdot 74.\] done
clear
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question_answer30)
At resonance which of the following physical quantity is maximum?
A)
Impedance done
clear
B)
Current done
clear
C)
Both [a] and [b] done
clear
D)
Neither [a] nor [b] done
clear
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question_answer31)
Directions : (31-35) |
LC Circuit |
An LC circuit also called a resonant circuit, tank circuit or tuned circuit is an electric circuit consisting of an inductor repesented by the letter L and a capacitor, represented by the letter C connected together. An LC circuit is an idealized model since it assumes there is no dissipation of energy due to resistance. |
An LC circuit contains a 20 mH inductor and a \[50\mu F\] capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0 |
|
The total energy stored initially is
A)
5 J done
clear
B)
3 J done
clear
C)
10 J done
clear
D)
1 J done
clear
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question_answer32)
The natural frequency of the circuit is
A)
\[159\centerdot 24\,Hz\] done
clear
B)
\[200\centerdot 12\,Hz\] done
clear
C)
\[110\centerdot 25\,Hz\] done
clear
D)
95 Hz done
clear
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question_answer33)
At what time is the energy stored completely electrical?
A)
T, 5T, 9T done
clear
B)
\[\frac{T}{2},\frac{5T}{2},\frac{9T}{2}\] done
clear
C)
0, T, 2T, 3T done
clear
D)
\[0,\frac{T}{2},T,\frac{3T}{2}\] done
clear
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question_answer34)
At what time is the energy stored completely magnetic?
A)
\[\frac{T}{2},\frac{3T}{2},\frac{T}{4}\] done
clear
B)
\[\frac{T}{3},\frac{T}{9},\frac{T}{12}\] done
clear
C)
\[0,\,2T,\,3T\] done
clear
D)
\[\frac{T}{4},\,\frac{3T}{4},\,\frac{5T}{4}\] done
clear
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question_answer35)
The value of \[{{X}_{L}}\] is
A)
\[20\Omega \] done
clear
B)
\[40\Omega \] done
clear
C)
\[60\Omega \] done
clear
D)
\[50\Omega \] done
clear
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question_answer36)
Directions : (36-40) |
Step-Down Transformer in the Transmission of Electric Power |
Step-down transformers are used to decrease or step-down voltages. These are used when voltages need to be lowered for use in homes and factories. |
A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is \[5\centerdot 5\,\Omega \] per km. The town gets power from the line through a 4000 - 200 V step-down transformer at a sub-station in the town. |
|
The value of total resitance of the wire is
A)
\[25\,\Omega \] done
clear
B)
\[30\Omega \] done
clear
C)
\[35\Omega \] done
clear
D)
\[15\Omega \] done
clear
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question_answer37)
The line power loss in the from of heat is
A)
550 kW done
clear
B)
650 kW done
clear
C)
600 kW done
clear
D)
700 kW done
clear
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question_answer38)
How much power must the plant supply, assuming there is negligible power loss due to leakage ?
A)
600 kW done
clear
B)
1600 kW done
clear
C)
500 W done
clear
D)
1400 kW done
clear
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question_answer39)
The voltage drop in the power line is
A)
1700 V done
clear
B)
3000 V done
clear
C)
2000 V done
clear
D)
2800 V done
clear
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question_answer40)
The total value of transmitted from the plant is
A)
500 V done
clear
B)
4000 V done
clear
C)
3000 V done
clear
D)
7000 V done
clear
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question_answer41)
Directions : (41-45) |
Power Associated with LCR Circuit |
In an a.c. circuit, values of voltage and current change every instant. Therefore power of an a.c. circuit at any instant is the product of instantaneous voltage (E) and instantaneous current (I). The average power supplied to a pure resistance R over a complete cycle of a.c. is \[P={{E}_{v}}{{I}_{v}}\], when circuit is inductive, average power per cycle is \[{{E}_{v}}{{I}_{v}}\cos \phi \]. |
|
In an a.c. circuit, 600 mH inductor and a \[50\mu F\] capacitor are connected in series with \[10\Omega \] resistance. The a.c.c supply to the circuit is 230 V, 60 Hz. |
The average power transferred per cycle to resistance is
A)
\[10\centerdot 42W\] done
clear
B)
\[15\centerdot 25W\] done
clear
C)
\[17\centerdot 42W\] done
clear
D)
\[13\centerdot 45W.\] done
clear
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question_answer42)
The average power transferred per cycle to capacitor is
A)
zero done
clear
B)
\[10\centerdot 42W\] done
clear
C)
\[17\centerdot 42W\] done
clear
D)
15 W done
clear
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question_answer43)
The average power transferred per cycle to inductor is
A)
25 W done
clear
B)
\[17\centerdot 42W\] done
clear
C)
\[16\centerdot 52W\] done
clear
D)
zero done
clear
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question_answer44)
The total power transferred per cycle by all the three circuit element is
A)
\[17\centerdot 42W\] done
clear
B)
\[10\centerdot 45W\] done
clear
C)
\[12\centerdot 45W\] done
clear
D)
zero done
clear
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question_answer45)
The electrical energy spent in running the circuit for one hour is
A)
\[7\centerdot 5\times {{10}^{5}}Joule\] done
clear
B)
\[10\times {{10}^{3}}Joule\] done
clear
C)
\[9\centerdot 4\times {{10}^{3}}Joule\] done
clear
D)
\[6\centerdot 2\times {{10}^{4}}Joule\] done
clear
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question_answer46)
Directions : (46-50) |
Transformer |
A transformer is an electrical device which is used for changing the a.c. voltages. It is based on the phenomenon of mutual induction i.e., whenever the amount of magnetic flux linked with a coil changes, an e.m.f. is induced in the neighbouring coil. For an ideal transformer, the resistances of the primary and secondary windings are negligible. |
|
In can be shown that \[\frac{{{E}_{s}}}{{{E}_{p}}}=\frac{{{I}_{p}}}{{{I}_{s}}}=\frac{{{n}_{s}}}{{{n}_{p}}}=k\] |
where the symbols have their standard meanings For a step up transformer, \[{{n}_{s}}>{{n}_{p}};\,{{E}_{s}}>{{E}_{p}}\,;\,k>1\,;\,\] |
\[\therefore \,\,\,{{I}_{s}}<{{I}_{p}}\] |
For a step down transformer, \[{{n}_{s}}<{{n}_{p}};\,{{E}_{s}}<{{E}_{p}};\,k<1\] |
The above relations are on the assumptions that efficiency of transformer is 100%. |
Infact, efficiency \[\eta =\frac{output\,power}{input\,power}=\frac{{{E}_{s}}\,{{I}_{s}}}{{{E}_{p}}\,{{I}_{p}}}\] |
Which of the following quanity remains constant in an ideal transformer?
A)
Current done
clear
B)
Voltage done
clear
C)
Power done
clear
D)
All of these. done
clear
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question_answer47)
Transformer is used to
A)
convert ac to dc voltage done
clear
B)
convert dc to ac voltage done
clear
C)
obtain desired dc power done
clear
D)
obtain desired ac voltage and current. done
clear
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question_answer48)
The number of turns in primary coil of a transformer is 20 and the number of turns in a secondary is 10. If the voltage across the primary is 220 ac V, what is the voltage across the seconary ?
A)
100 acV done
clear
B)
120 ac V done
clear
C)
110 acV done
clear
D)
220 ac V done
clear
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question_answer49)
In a transformer the number of primary turns is four times that of the seconary turns. Its primary is connected to an a. c. source of voltage V. Then
A)
current through its seconary is about four times that of the current through its primary done
clear
B)
voltage across its secondary is about four times that of the voltage across its primary done
clear
C)
voltage across its seconary is about two times that of the voltage across its primary done
clear
D)
voltage across its seconary is about \[\frac{1}{2\sqrt{2}}\] times that of the voltage across its primary. done
clear
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question_answer50)
A transformer is used to light 100 W - 110 V lamp from 220 V mains. If the main current is \[0\centerdot 5A\], the efficiency of the transformer is
A)
95% done
clear
B)
99% done
clear
C)
90% done
clear
D)
96%. done
clear
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