1. Let us consider two solenoids A and B, made from same magnetic material of relative permeability μ_r and equal area of cross-section. Length of A is twice that of B and the number of turns per unit length in A is half that of B. The ratio of self inductances of the two solenoids, L_A : L_B is

(1).1 : 2

(2). 2 : 01

(3). 8 : 01

(4). 1 : 8

2. In the circuit shown below, the inductance L is connected to an ac source. The current flowing in the circuit is I = I0 sin ωt. The voltage drop (VL) across L is

(1).\(wLI_0sinwt\)

(2). \(\frac{I_0}{wL}sinwt\)

(3). \(\frac{I_0}{wL}coswt\)

(4). \(wLI_0coswt\)

3. A step up transformer is connected to an ac mains supply of 220V to operate at 11000V, 88 watt. The current in the secondary circuit, ignoring the power loss in the transformer, is

(1).8 mA

(2). 4 mA

(3). 0.4 A

(4). 4 A

4. The amplitude of the charge oscillating in a circuit decreases exponentially as \(Q = Q_0e{−Rv2L}\) , where Q₀ is the charge at t = 0 s . The time at which charge amplitude decreases to 0.50 Q₀ is nearly:[Given that R = 1.5Ω, L = 12 mH, ln(2) = 0.693]

(1).19.01 ms

(2). 11.09 ms

(3). 19.01 s

(4). 11.09 s

5. In an ideal transformer, the turns ratio is \(\frac{N_P}{N_S} = \frac{1}{2}\). The ratio \(V_S : V_P\) is equal to (the symbols carry their usual meaning) :

(1).1 : 2

(2). 2 : 1

(3). 1 : 1

(4). 1 : 4

6. A 10μF capacitor is connected to a 210V,50Hz source as shown in figure. The peak current in the circuit is nearly (π = 3.14) :

(1).0.58 A

(2). 0.93 A

(3). 1.20 A

(4). 0.35 A

7. The net magnetic flux through any closed surface is

(1).Positive

(2). Infinity

(3). Negative

(4). Zero

8. The magnetic energy stored in an inductor of inductance 4μH carrying a current of 2A is

(1).4 mJ

(2). 8 mJ

(3). 8 μJ

(4). 4 μJ

9. In a series LCR circuit, the inductance L is 10mH,capacitance C is 1μF and resistance R is 100Ω. The frequency at which resonance occurs is

(1).15.9 kHz

(2). 1.59 rad∕ s

(3). 1.59 kHz

(4). 15.9 rad∕ s

10. A 12V, 60W lamp is connected to the secondary of a step-down transformer, whose primary is connected to ac mains of 220V. Assuming the transformer to be ideal, what is the current in the primary winding?

(1).2.7 A

(2). 3.7 A

(3). 0.37 A

(4). 0.27 A

11. The net impedance of circuit (as shown in figure) will be

(1).15 Ω

(2). 5√5 Ω

(3). 25 Ω

(4). 10√2 Ω

12. An ac source is connected in the given circuit. The value of φ will be :

(1).\(60^\circ\)

(2). \(90^\circ\)

(3). \(30^\circ\)

(4). \(45^\circ\)

13. If Z₁ and Z₂ are the impedances of the given circuits (a) and (b) as shown in figures, then choose the correct option

(1).\(Z_1 < Z_2\)

(2). \(Z_1 = Z_2\)

(3). \(Z_1 + Z_2 = 20\, Ω\)

(4). \(Z_1 > Z_2\)

14. The maximum power is dissipated for an ac in a/an:

(1).resistive circuit

(2). LC circuit

(3). inductive circuit

(4). capacitive circuit

15. An emf is generated by an ac generator having 100 turn coil, of loop area 1 m². The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of 0.05T perpendicular to the axis of rotation of the coil. The maximum value of emf is :-

(1).3.14 V

(2). 31.4 V

(3). 62.8 V

(4). 6.28 V

16. For very high frequencies, the effective impedance of the circuit (shown in the figure) will be :-

(1).4 Ω

(2). 6 Ω

(3). 1 Ω

(4). 3 Ω

17. The magnetic flux linked to a circular coil of radius R is:φ = 2t³ + 4t² + 2t + 5 WbThe magnitude of induced emf in the coil at t = 5s is:

(1).192 V

(2). 108 V

(3). 197 V

(4). 150 V

18. Given below are two statements.Statement I:In an ac circuit, the current through a capacitor leads the voltage across it.Statement II:In a.c circuits containing pure capacitance only, the phase difference between the current and the voltage is π.In the light of the above statements, choose the most appropriate answer from the options given below

(1).Statement I is incorrect but Statement II is correct

(2). Both Statement I and Statement II are correct

(3). Both Statement I and Statement II are incorrect

(4). Statement I is correct but Statement II is incorrect

19. An inductor of inductance 2 mH is connected to a 220V, 50 Hz a.c. source. Let the inductive reactance in the circuit is X₁. If a 220V dc source replaces the ac source in the circuit, then the inductive reactance in the circuit is X₂. X₁ and X₂ resspectively are

(1).0.628Ω, infinity

(2). 6.28Ω, zero

(3). 6.28Ω, infinity

(4). 0.628Ω, zero

20. A standard filament lamp consumes 100W when connected to 200V ac mains supply. The peak current through the bulb will be:

(1).2A

(2). 0.707A

(3). 1A

(4). 1.41A

21. The peak voltage of the ac source is equal to

(1).The value of voltage supplied to the circuit

(2). The rms value of the ac source

(3). \(\sqrt{2}\) times the rms value of the ac source

(4). \(\frac{1}{\sqrt{2}}\) times the rms value of the ac source

22. A square loop of side 1m and resistance 1Ω is placed in a magnetic field of 0.5 T . If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is

(1).2 weber

(2). 0.5 weber

(3). 1 weber

(4). Zero weber

23. A series LCR circuit with inductance 10H , capacitance 10μF , resistance50Ω is connected to an ac source of voltage, V = 200 sin(100t) volt. Ifthe resonant frequency of the LCR circuit is v₀ and the frequency of theac source is v, then

(1).v₀ = v = 50 Hz

(2). v₀ = v = 50/π Hz

(3). v₀ = 50/π Hz, v = 50 Hz

(4). v = 100H z; v₀ = 100/π Hz

24. A big circular coil of 1000 turns and average radius 10m is rotating about its horizontal diameter at 2 rad⁻¹. If the vertical component of earth's magnetic field at that place is 2 × 10^−5T and electrical resistance of the coil is 12.56Ω, then the maximum induced current in the coil will be

(1).0.25 A

(2). 1.5 A

(3). 1 A

(4). 2 A

25. An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance ' R ' are connected in series to an ac source of potential difference 'V' volts as shown in figure. Potential difference across L, C and R is 40V , 10 V and 40V ,respectively. The amplitude of current flowing through C R series circuit is 10√2A. The impedance of the circuit is

(1).4√2Ω

(2). 5√2Ω

(3). 4Ω

(4). 5Ω

26. A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

(1).0.2 A

(2). 0.4 A

(3). 2 A

(4). 4 A

27. A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be

(1).25 rad/s and 75 rad/s

(2). 50 rad/s and 25 rad/s

(3). 46 rad/s and 54 rad/s

(4). 42 rad/s and 58 rad/s

28. Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ > R₂, the mutual inductance M between them will be directly proportional to

(1).\(\frac{R_1}{R_2}\)

(2). \(\frac{R_2}{R_1}\)

(3). \(\frac{R_1^2}{R_2}\)

(4). \(\frac{R_2^2}{R_1}\)

29. A 40μ F capacitor is connected to a 200V , 50H z ac supply. The rms value of the current in the circuit is, nearly:

(1).2.05A

(2). 2.5A

(3). 25.1A

(4). 1.7A

30. A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed from the circuit, the phase difference is again π/3 between current and voltage. The power factor of the circuit is:

(1).0.5

(2). 1.0

(3). -1.0

(4). zero

31. In which of the following devices, the eddy current effect is not used?

(1).electric heater

(2). induction furnace

(3). magnetic braking in train

(4). electromagnet

32. A 800 turn coil of effective area 0.05m² is kept perpendicular to amagnetic field 5 × 10⁻⁵ T. When the plane of the coil is rotated by 90∘ around any of its coplanar axis in 0.1 s, the emf induced in the coil will be

(1).0.02V

(2). 2V

(3). 0.2V

(4). 2 × 10⁻³V

33. A circuit when connected to an AC source of 12V gives a current of 0.2A. The same circuit when connected to a DC source of 12V , gives acurrent of 0.4A. The circuit is

(1).series LR

(2). series RC

(3). series LC

(4). series LCR

34. A cycle wheel of radius 0.5m is rotated with constant angular velocity of10rad ∕ s in a region of magnetic field of 0.1T which is perpendicular to the plane of the wheel. The EMF generated between its centre and the rim is,

(1).0.25V

(2). 0.125V

(3). 0.5V

(4). zero

35. The magnetic potential energy stored in a certain inductor is 25mJ , when the current in the inductor is 60mA. This inductor is of inductance

(1).0.138H

(2). 138.88H

(3). 1.389H

(4). 13.89H

36. An inductor 20mH , a capacitor 100μF and a resistor 50Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is

(1).0.79W

(2). 0.43W

(3). 2.74W

(4). 1.13W

37. A long solenoid of diameter 0.1 m has 2 × 10⁴ turns per metre. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10π²Ω, the total charge flowing through the coil during this time is

(1).16 μC

(2). 32 μC

(3). 16 πμC

(4). 32 π μC

38. Figure shows a circuit that contains three identical resistors with resistance R = 9.0Ω each, two identical inductors with inductance L =2.0 mH each, and an ideal battery with emf ε = 18V . The current i through the battery just after the switch closed is

(1).0.2 A

(2). none of the above

(3). 0 A

(4). 2 mA

39. An inductor 20 mH, a capacitor 50 μF and a resistor 40 Ω are connected in series across a source of emf V = 10sin340t. The power loss in A.C. circuit is

(1).0.76 W

(2). 0.89 W

(3). 0.51 W

(4). 0.67 W

40. A small signal voltage V (t) = V₀sinωt is applied across an ideal capacitor C

(1).Current /(f) is in phase with voltage V(t).

(2). Current /(f) leads voltage V(t) by 180°.

(3). Current /(f), lags voltage V(t) by 90°

(4). Over a full cycle the capacitor C does not consume any energy from the voltage source

41. A long solenoid has 1000 turns. When a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is 4 × 10 ⁻³ Wb. The self-inductance of the solenoid is

(1).2 H

(2). 1 H

(3). 4 H

(4). 3 H

42. Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication ?

(1).R = 20Ω, L = 1.5H , C = 35μF

(2). R = 25Ω, L = 2.5H , C = 45μF

(3). R = 15Ω, L = 3.5H , C = 30μF

(4). R = 25Ω, L = 1.5H , C = 45μF

43. A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate \(\frac{\vec{dB}}{dt}\) . Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the e.m.f. generated is

(1).Zero in loop 1 and zero in loop 2

(2). \(-\frac{\vec{dB}}{dt}\pi r^2\) in loop 1 and \(-\frac{\vec{dB}}{dt}\pi r^2\) in loop 2

(3). \(\frac{\vec{dB}}{dt}\pi R^2\) in loop 1 and zero in loop 2

(4). \(\frac{\vec{dB}}{dt}\pi r^2\) in loop 1 and zero in loop 2

44. The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L-C-R circuit.The power factor of this circuit is

(1).0.4

(2). 0.5

(3). 0.8

(4). 1.0

45. A resistance 'P' 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

(1).\(P \left(\frac{R}{Z}\right)\)

(2). \(P\)

(3). \(P \left(\frac{R}{Z}\right)^2\)

(4). \(P \sqrt{\frac{R}{Z}}\)

46. A conducting square frame of side ‘a ’ and a long straight wire carrying current I are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity ‘V’. The emf induced in the frame will be proportional to

(1).\(\frac{1}{\left(2x + a\right)^2}\)

(2). \(\frac{1}{\left(2x - a\right)\left(2x +a \right)}\)

(3). \(\frac{1}{x^2}\)

(4). \(\frac{1}{\left(2x - a\right)^2}\)

47. A series R-C circuit is connected to an alternating voltage source.Consider two situations(a) When capacitor is air filled.(b) When capacitor is mica filled. Current through resistor is i and voltage across capacitor is V then

(1).i_a > i_b

(2). V_a = V_b

(3). V_a < V_b

(4). V_a > V_b

48. An electron moves on a straight line path X Y as shown. The abed is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil?

(1).The current will reverse its direction as the electron goes past the coil

(2). No current induced

(3). abed

(4). adcb

49. A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure.The potential difference developed across the ring when its speed is v, is

(1).zero

(2). \(\frac{Bv\pi r^2}{2}\) and P is at higher potential

(3). \(\pi rBv\) and R is at higher potential

(4). \(2rBv\) and R is at higher potential

50. A transformer having efficiency of 90% is working on 200 V and 3 kW power supply. If the current in the secondary coil is 6 A, the voltage across the secondary coil and the current in the primary coil respectively are

(1).300 V, 15 A

(2). 450 V,15 A

(3). 450 V, 13.5 A

(4). 600 V, 15 A