The Thevenin s equivalent of a circuit operating at = 5 rad/s, has Voc = 3.71 15.9 V and Z0 = 2.38 j 0.667 &ohm; . At this frequency, the minimal realization of the Thevenin s impedance will have a

resistor and a capacitor and an inductor

A series RLC circuit s observed at two frequencies. At 1 = 1 k rad/s, we note that source voltage V1 = 100 0 V results in current I1 = 0.03 31 A. At 2 = 2 krad/s, the source volt age V2 = 100 0 V results in a current I2 = 2 0 A. The closest values for R, L, C out of the following options are

R = 50 &ohm; ; L = 50mH ; C = 5 F;

R = 50 &ohm; ; L = 25mH ; C =10 F;

R = 50 &ohm; ; L =10mH ; C = 25 F;

R = 50 &ohm; ; L = 50mH ; C = 5 F;

R = 50 &ohm; ; L = 5mH ; C = 50 F;

A battery charger can drive a current of 5 A into a 1 ohm resistance connected at its output teminals. If it is able to charge an ideal 2 V battery at 7 A rate, then its Thevenin s equivalent will be

1.25 V in parallel with 1.5 ohms

The number of independent loops for a network with n nodes and b branch is

independent of the number of nodes

A two terminal black box contains one of the R.L.C. elements. The black box is connected to a 220 volts A.C. supply. The current through the source is I. When a capacitance of 0.1F is inserted in the series between the source and the box, the current through the source is 2I. The element is

it is not possible to determine the element.

Two incandescent light bulbs of 40 W and 60W rating are connected in series across the mains. Then

the bulbs together consume 100 W

the bulbs together consume 50 W

A connected network of N > 2 nodes has at most one branch directly connecting any pair of nodes. The graph of the network

must have at least N branches for one or more closed paths to exist

can have an unlimited number of branches

can only have at most N branches

can have a minimum number of branches not decided by N.

Two coils having equal resistance but different inductances are connected in series. the time constant of the series combination is the

geometric mean of the time constants of the individual coils

sum of the time constants of the individual coils

average of the time constants of individual coils

geometric mean of the time constants of the individual coils

product of the time constants of the individual coils

The Thevenin s equivalent of a circuit operating at = 5 rad/s, has V

resistor and a capacitor and an inductor

72 + Mcqs in Electric circuits miscellaneous Page 1 McqOptions

1.	A series RLC circuit consisting of R = 10 ohms, X_L = 20 ohms and X_c = 20 ohms is connected across an ac supply of 100 V (rms). The magnitude and phase angle (with reference to supply voltage) of the voltage across the inductive coil are respectively
A.	100 V, 90
B.	100 V, 90
C.	200 V, 90
D.	200 V, 90
Answer» E.

Discussion

2.	A 3 V dc supply with an internal resistance of 2 Ω supplies a passive non-linear resistance characterized by the relation V_NL = I² _NL. The power dissipated in the non-linear resistance is
A.	1.0 W
B.	1.5 W
C.	2.5 W
D.	3.0 W
Answer» B. 1.5 W

Discussion

3.	The Thevenin s equivalent of a circuit operating at = 5 rad/s, has V_oc = 3.71 15.9 V and Z₀ = 2.38 j 0.667 Ω . At this frequency, the minimal realization of the Thevenin s impedance will have a
A.	resistor and a capacitor and an inductor
B.	resistor and a capacitor
C.	resistor and an inductor
D.	capacitor and an inductor
Answer» C. resistor and an inductor

Discussion

4.	An average-reading digital multimeter reads 10 V when fed with a triangular wave, symmetric about the time-axis. For the same input an rmsreading meter will read
A.	20
B.	10
Answer» B. 10

Discussion

5.	A coil of 300 turns is wound on a non-magnetic core having a mean circumference of 300 mm and a cross-sectional area of 300 mm². The inductance of the coil corresponding to a magnetizing current of 3A will be (Given that ₀ = 4 10⁷ H/m)
A.	37.68 H
B.	113.04 H
C.	37.68 mH
D.	113.04 mH
Answer» C. 37.68 mH

Discussion

6.	A capacitor consists of two metal plates each 500 500 mm² and spaced 6 mm apart. The space between the metal plates is filled with a glass plate of 4 mm thickness and a layer of paper of 2 mm thickness. The relative permittivities of the glass and paper are 8 and 2 respectively. Neglecting the fringing effect, the capacitance will be (Given that ₀ = 8.85 10¹² F/m)
A.	983.33 pF
B.	1475 pF
C.	6637.5 pF
D.	9956.25 pF
Answer» C. 6637.5 pF

Discussion

7.	Divergence of the vector field V (x, y, z) = (x cos xy + y) i + (y cos xy) j + (sin z² + x² + y²) k is
A.	2z cos z
B.	sin xy + 2z cos z
C.
D.	x sin xy cos z
E.	none of these
Answer» B. sin xy + 2z cos z

Discussion

8.	Two point charges Q₁ = 10 C and Q₂ = 20 C are placed at coordinates (1, 1, 0) and ( 1, 1, 0) respect ively. The total electric flux passing through a plane z = 20 will be
A.	7.5 C
B.	13.5 C
C.	15.0 C
D.	22.5 C
Answer» D. 22.5 C

Discussion

9.

Consider the following statements with reference to the equation p
t

1. This is a point form of the continuity equation
2. Divergence of current density is equal to the decrease of charge per unit volume per unit at every point
3. This is Max well's divergence equation
4. This represents the conservation of charge Select the correct answer:

A.

Only 2 and 4 are true

B.

1, 2 and 3 are true

C.

2, 3 and 4 are true

D.

1, 2 and 4 are true

Answer» E.

Discussion

10.	An incandescent lamp is marked 40W, 240V. If resistance at room temperature (26 C) is 120 Ω and temperature coefficient of resistance is 4.5 10^{3/ C} , then its ON state filament temperature in C is approximately ___________.
A.	1171
B.	2471
C.	1417
D.	All of the above
Answer» C. 1417

Discussion

11.	Current I₁, I₂ and I₃ meet at a junction (node) in a circuit. All currents are marked as entering the node. If I₁ = 6 sin ( t) mA and I₂ = 8 cos ( t) mA, then I 3 will be
A.	10 cos ( t + 36.87) mA
B.	14 cos ( t + 36.87) mA
C.	14 sin ( t + 36.87) mA
D.	10 cos ( t + 36.87) mA
Answer» E.

Discussion

12.	The maximum value of mutual inductance of two inductively coupled coils with selfinductance, L₁ = 49 mH and L₂ = 81 mH is
A.	130 mH
B.	63 mH
C.	32 mH
D.	3969 mH
Answer» C. 32 mH

Discussion

13.	Divergence of the three-dimensional radial vector field r is
A.	3
B.	1 / r
Answer» B. 1 / r

Discussion

14.

The driving point impedance Z(s) = s + 2
s + 2

The system is initially at rest. For a voltage signal of unit step, the current i (t) through the impedance Z is given by

A.

2 - e

B.

3 - 2 e

Answer» D.

Discussion

15.	After closing the switch S at t = 0, the current i (t) at any instant t in the network shown in the given figure will be
A.	10 + 10 e
B.
C.	10 10 e
D.	10 + 10 e
E.	10 10 e
Answer» E. 10 10 e

Discussion

16.

Consider a function f = 1 r , where r is distance from origin and r is unit vector.
r²
, The divergence of this function over a sphere of radius R, which includes origin is.

A.

0

B.

2

C.

4

D.

R .

Answer» D. R .

Discussion

17.	In an unbalanced three phase system, phase current I_a = 1 ( 90 ) pu, negative sequence current I_b2 = 4 ( 150 )pu, zero sequence current I_C0 = 3 90 pu. The magnitude of phase current I_b in pu is
A.	1.00
B.	7.81
C.	11.53
D.	13.00
Answer» D. 13.00

Discussion

18.	A series RLC circuit s observed at two frequencies. At ₁ = 1 k rad/s, we note that source voltage V₁ = 100 0 V results in current I₁ = 0.03 31 A. At ₂ = 2 krad/s, the source volt age V₂ = 100 0 V results in a current I₂ = 2 0 A. The closest values for R, L, C out of the following options are
A.	R = 50 &ohm; ; L = 25mH ; C =10 F;
B.	R = 50 &ohm; ; L =10mH ; C = 25 F;
C.	R = 50 &ohm; ; L = 50mH ; C = 5 F;
D.	R = 50 &ohm; ; L = 5mH ; C = 50 F;
Answer» C. R = 50 &ohm; ; L = 50mH ; C = 5 F;

Discussion

19.

The system function H(s) = 1
s + 1

For an input signal cos t, the steady state response is

A.

cos t

Answer» B.

Discussion

20.	A series LCR circuit consisting of R = 10 ohms [X_L] = 20 ohms is connected across an a.c. supply of 200 V rms. The rms voltage across the capacitor is
A.	200 90 V
B.	200 + 90 V
C.	400 + 90 V
D.	400 90 V
Answer» E.

Discussion

21.	In respect of the 2-port network shown in the given figure, admittance parameters are : Y₁₁ = 8 mho, Y₁₂ = Y₂₁ = 6 mho and Y₂₂ = 6 mho. The values of Y_A, Y_B and Y_C (in units of mho) will be respectively
A.	2, 6 and 6
B.	2, 6 and 0
C.	2, 0 and 6
D.	2, 6 and 8
Answer» D. 2, 6 and 8

Discussion

22.	A two-port network is defined by the relations I₁ = 2V₁ + V₂, I₂ = 2V₁ + 3V₂ Then z₁₂ is
A.	2 &ohm;
B.	1 &ohm;
Answer» E.

Discussion

23.	A battery charger can drive a current of 5 A into a 1 ohm resistance connected at its output teminals. If it is able to charge an ideal 2 V battery at 7 A rate, then its Thevenin s equivalent will be
A.	7.5 V in series with 0.5 ohm
B.	12 V in series with 1.5 ohms
C.	7.5 V in parallel with 0.5 ohm
D.	1.25 V in parallel with 1.5 ohms
Answer» C. 7.5 V in parallel with 0.5 ohm

Discussion

24.	H ow many 200W/220V incandescent lamps connected in series would consume the same total power as a single 100W/220V incandescent lamp?
A.	not possible
B.	4
C.	3
D.	2
Answer» E.

Discussion

25.	A series RLC circuit consisting of R = 10 ohms, X
A.	100 V, 90
B.	100 V, 90
C.	200 V, 90
D.	200 V, 90
Answer» E.

Discussion

26.	The number of independent loops for a network with n nodes and b branch is
A.	n 1
B.	b n
C.	b n + 1
D.	independent of the number of nodes
Answer» D. independent of the number of nodes

Discussion

27.	A two terminal black box contains one of the R.L.C. elements. The black box is connected to a 220 volts A.C. supply. The current through the source is I. When a capacitance of 0.1F is inserted in the series between the source and the box, the current through the source is 2I. The element is
A.	a resistance
B.	an inductance
C.	a capacitance of 0.5F
D.	it is not possible to determine the element.
Answer» C. a capacitance of 0.5F

Discussion

28.	The maximum value of mutual inductance of two inductively coupled coils with selfinductance, L
A.	130 mH
B.	63 mH
C.	32 mH
D.	3969 mH
Answer» C. 32 mH

Discussion

29.	Two incandescent light bulbs of 40 W and 60W rating are connected in series across the mains. Then
A.	the bulbs together consume 100 W
B.	the bulbs together consume 50 W
C.	the 60 W bulb glows brighter
D.	the 40 bulb glows brighter
Answer» E.

Discussion

30.	Current I
A.	10 cos ( t + 36.87) mA
B.	14 cos ( t + 36.87) mA
C.	14 sin ( t + 36.87) mA
D.	10 cos ( t + 36.87) mA
Answer» E.

Discussion

31.	If the number of branches in a network is B, the number of nodes is N and the number of dependent loops is L, then the number of independent node equations will be
A.	N + L 1
B.	B 1
C.	B N
D.
E.	N 1
Answer» E. N 1

Discussion

32.	A connected network of N > 2 nodes has at most one branch directly connecting any pair of nodes. The graph of the network
A.	must have at least N branches for one or more closed paths to exist
B.	can have an unlimited number of branches
C.	can only have at most N branches
D.	can have a minimum number of branches not decided by N.
Answer» E.

Discussion

33.	A certain network consists of two ideal voltage sources and a large number of ideal resistors. The power consumed in one of the resistor is 4 W when either of the two sources is active and the other is replaced by a short circuit. The power consumed by the same resistor when both the sources are simultaneously active would be
A.	zero or 16 W
B.	4 W or 8 W
C.	zero or 8 W
D.	8 W or 16 W
Answer» D. 8 W or 16 W

Discussion

34.	A load that has a resistance of 10 ohms is to be connected to a supply that has a constant voltage of 120 volts. If it is desired that the currrent to the load be varied from 3 to 5 amperes, what are the resistance and the current rating of the series rheostat that permit this variation?
A.	30 ohms, 5A
B.	10 ohms, 10A
C.	20 ohms, 10A
D.	20 ohms, 10A
Answer» B. 10 ohms, 10A

Discussion

35.

The system function H(s) = 1
s + 1

A.

B.

cos t

C.

D.

Answer» B. cos t

Discussion

36.	In respect of the 2-port network shown in the given figure, admittance parameters are :
A.	2, 6 and 6
B.	2, 6 and 0
C.	2, 0 and 6
D.	2, 6 and 8
Answer» D. 2, 6 and 8

Discussion

37.	An ideal transformer has turns ratio of 2 : 1. Considering high voltage side as port 1 and low voltage side as port 2, then transmission line parameters of transformer will be
A.	<table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>0</td><td></td><td></td><td>-2</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td></tr><tr><td>0.5</td><td></td><td></td><td>0</td></tr></table>
B.	<table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>-2</td><td></td><td></td><td>0</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td></tr><tr><td>0</td><td></td><td></td><td>-0.5</td></tr></table>
C.	<table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>2</td><td></td><td></td><td>0</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td></tr><tr><td>0</td><td></td><td></td><td>-0.5</td></tr></table>
D.	<table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>0.5</td><td></td><td></td><td>0</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td></tr><tr><td>0</td><td></td><td></td><td>2</td></tr></table>
Answer» D. <table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>0.5</td><td></td><td></td><td>0</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td></tr><tr><td>0</td><td></td><td></td><td>2</td></tr></table>

Discussion

38.	Two coils having equal resistance but different inductances are connected in series. the time constant of the series combination is the
A.	sum of the time constants of the individual coils
B.	average of the time constants of individual coils
C.	geometric mean of the time constants of the individual coils
D.	product of the time constants of the individual coils
Answer» C. geometric mean of the time constants of the individual coils

Discussion

39.

With the usual notations, a two-port resistive network satisfies the condition A = D = 3 B = 4 C
2 3

A.

B.

C.

D.

Answer» C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2"> </td></tr><tr><td style="text-align: center;">3</td></tr></table>

Discussion

40.	A two-port network is defined by the relations I
A.	2 &ohm;
B.	1 &ohm;
C.	<table><tr><td rowspan="2">-</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> &ohm;</td></tr><tr><td style="text-align: center;">2</td></tr></table>
D.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> &ohm;</td></tr><tr><td style="text-align: center;">4</td></tr></table>
Answer» E.

Discussion

41.	Five cells are connected in series in a row and then four such rows are connected in parallel to feed the current to a resistive load of 1.25 Ω . Each cell has emf of 1.5 V with internal resistance of 0.2 Ω . The current through the load will be _____ .
A.	1 A
B.	5 A
C.	15 A
D.	None of the above
Answer» C. 15 A

Discussion

42.	When two coupled coils of equal self-inductance are connected in series in one way the net inductance is 12 mH, and when they are connected in the other way, the net inductance is 4 mH. The maxiumum value of net inductance when they are connected in parallel in a suitable way is _________ mH
A.	3 mH
B.	5 mH
C.	9 mH
D.	10 mH
Answer» B. 5 mH

Discussion

43.	A 35 V source is connected to a series circuit at 600 ohms and R as shown. If a voltmeter at internal resistance 1.2 kilo ohms is connected across 600 ohm resistor it reads 5 V. The value of R is ______k Ω .
A.	1.4 k&ohm;
B.	2.0 k&ohm;
C.	2.4 k&ohm;
D.	None of these
Answer» D. None of these

Discussion

44.	The energy stored in the magnetic field at a solenoid 30 cm long and 3 cm diameter wound with 1000 turns of wire carrying a current at 10 A, is ________ Joules
A.	0.148 or 0.15 Joules
B.	11.148 or 11.2 Joules
C.	10.120 or 10.15 Joules
D.	None of the above
Answer» B. 11.148 or 11.2 Joules

Discussion

45.	At a certain current, the energy stored in iron cored coil is 1000 J and its copper loss is 2000 W. The time constant (in seconds) of the coil is_____
A.	0
B.	1
C.	2
D.	3
Answer» C. 2

Discussion

46.	A resistance R Ω and inductance of L H are connected across 240 V, Hz supply. Power dissipated in the circuit is 300 W and the voltage across R is 100 V. In order to improve the power fact or to unity, the capacitor that is to be connect ed in series should have a val ue of _______ F
A.	11.5 F.
B.	13.7 F.
C.	12.5 F.
D.	43.7 F.
Answer» E.

Discussion

47.	Two coils in differential connection have self inductance of 2 mH and 4 mH and a mutual inductance of 0.15 mH. The equivalent inductance of the combination is _____ mH
A.	1.7 mH
B.	3.0 mH
C.	5.7 mH
D.	1.7 mH
Answer» D. 1.7 mH

Discussion

48.	The Thevenin s equivalent of a circuit operating at = 5 rad/s, has V
A.	resistor and a capacitor and an inductor
B.	resistor and a capacitor
C.	resistor and an inductor
D.	capacitor and an inductor
Answer» C. resistor and an inductor

Discussion

49.	Two point charges Q
A.	7.5 C
B.	13.5 C
C.	15.0 C
D.	22.5 C
Answer» D. 22.5 C

Discussion

50.	A 3 V dc supply with an internal resistance of 2 Ω supplies a passive non-linear resistance characterized by the relation V
A.	1.0 W
B.	1.5 W
C.	2.5 W
D.	3.0 W
Answer» B. 1.5 W

Discussion

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Five cells are connected in series in a row and then four such rows are connected in parallel to feed the current to a resistive load of 1.25 Ω . Each cell has emf of 1.5 V with internal resistance of 0.2 Ω . The current through the load will be _____ .

When two coupled coils of equal self-inductance are connected in series in one way the net inductance is 12 mH, and when they are connected in the other way, the net inductance is 4 mH. The maxiumum value of net inductance when they are connected in parallel in a suitable way is _________ mH

A 35 V source is connected to a series circuit at 600 ohms and R as shown. If a voltmeter at internal resistance 1.2 kilo ohms is connected across 600 ohm resistor it reads 5 V. The value of R is ______k Ω .

The energy stored in the magnetic field at a solenoid 30 cm long and 3 cm diameter wound with 1000 turns of wire carrying a current at 10 A, is ________ Joules

At a certain current, the energy stored in iron cored coil is 1000 J and its copper loss is 2000 W. The time constant (in seconds) of the coil is_____

A resistance R Ω and inductance of L H are connected across 240 V, Hz supply. Power dissipated in the circuit is 300 W and the voltage across R is 100 V. In order to improve the power fact or to unity, the capacitor that is to be connect ed in series should have a val ue of _______ F

Two coils in differential connection have self inductance of 2 mH and 4 mH and a mutual inductance of 0.15 mH. The equivalent inductance of the combination is _____ mH

The Thevenin s equivalent of a circuit operating at = 5 rad/s, has V

Two point charges Q

A 3 V dc supply with an internal resistance of 2 Ω supplies a passive non-linear resistance characterized by the relation V

A series RLC circuit consisting of R = 10 ohms, X_L = 20 ohms and X_c = 20 ohms is connected across an ac supply of 100 V (rms). The magnitude and phase angle (with reference to supply voltage) of the voltage across the inductive coil are respectively

A 3 V dc supply with an internal resistance of 2 Ω supplies a passive non-linear resistance characterized by the relation V_NL = I² _NL. The power dissipated in the non-linear resistance is

The Thevenin s equivalent of a circuit operating at = 5 rad/s, has V_oc = 3.71 15.9 V and Z₀ = 2.38 j 0.667 Ω . At this frequency, the minimal realization of the Thevenin s impedance will have a

A coil of 300 turns is wound on a non-magnetic core having a mean circumference of 300 mm and a cross-sectional area of 300 mm². The inductance of the coil corresponding to a magnetizing current of 3A will be (Given that ₀ = 4 10⁷ H/m)

Divergence of the vector field V (x, y, z) = (x cos xy + y) i + (y cos xy) j + (sin z² + x² + y²) k is

Two point charges Q₁ = 10 C and Q₂ = 20 C are placed at coordinates (1, 1, 0) and ( 1, 1, 0) respect ively. The total electric flux passing through a plane z = 20 will be

An incandescent lamp is marked 40W, 240V. If resistance at room temperature (26 C) is 120 Ω and temperature coefficient of resistance is 4.5 10^{3/ C} , then its ON state filament temperature in C is approximately ___________.

Current I₁, I₂ and I₃ meet at a junction (node) in a circuit. All currents are marked as entering the node. If I₁ = 6 sin ( t) mA and I₂ = 8 cos ( t) mA, then I 3 will be

The maximum value of mutual inductance of two inductively coupled coils with selfinductance, L₁ = 49 mH and L₂ = 81 mH is

The driving point impedance Z(s) = s + 2
s + 2

The system is initially at rest. For a voltage signal of unit step, the current i (t) through the impedance Z is given by

Consider a function f = 1 r , where r is distance from origin and r is unit vector.
r²
, The divergence of this function over a sphere of radius R, which includes origin is.

In an unbalanced three phase system, phase current I_a = 1 ( 90 ) pu, negative sequence current I_b2 = 4 ( 150 )pu, zero sequence current I_C0 = 3 90 pu. The magnitude of phase current I_b in pu is

The system function H(s) = 1
s + 1

For an input signal cos t, the steady state response is

A series LCR circuit consisting of R = 10 ohms [X_L] = 20 ohms is connected across an a.c. supply of 200 V rms. The rms voltage across the capacitor is

In respect of the 2-port network shown in the given figure, admittance parameters are :
Y₁₁ = 8 mho, Y₁₂ = Y₂₁ = 6 mho and Y₂₂ = 6 mho. The values of Y_A, Y_B and Y_C (in units of mho) will be respectively

A two-port network is defined by the relations I₁ = 2V₁ + V₂, I₂ = 2V₁ + 3V₂ Then z₁₂ is

The system function H(s) = 1
s + 1

With the usual notations, a two-port resistive network satisfies the condition A = D = 3 B = 4 C
2 3