Self/Mutual Inductance & Eddy Currents — Practice Questions

Free NEET Physics multiple-choice questions on Self/Mutual Inductance & Eddy Currents. Attempt each question and reveal the answer with a full explanation.

The magnetic energy stored in an inductor of inductance 4 H carrying a current of 2 A is: 8 J 4 J 16 J 32 J Two coils A and B are placed close to each other. When the current in coil A changes by 2 A, the magnetic flux in B changes by 1 Wb. The mutual inductance between the coils is: 0.5 H 2 H 1 H 0.2 H The core of a transformer is laminated to reduce energy loss due to: Eddy currents Hysteresis Copper loss Flux leakage The self-inductance of a long solenoid cannot be increased by: Increasing the current through it Increasing the number of turns Using a soft iron core Increasing the cross-sectional area Which of the following is the unit of L/R ? Second Hertz Ohm Meter If the current in a primary coil changes from 2 A to 0 A in 0.1 s, and the mutual inductance between the two coils is 0.5 H, the induced emf in the secondary coil is: 10 V 5 V 0.5 V 2 V The self-inductance of a solenoid with N turns, length l and area A is L . If the core is replaced by a material of relative permeability r , the new self-inductance is: r L L/ r r 2 L "L" The magnetic energy stored in a solenoid of self-inductance L and current I is U . If the current is doubled, the stored energy becomes: 4U 2U U/2 8U Two coils of self-inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is: 4 mH 16 mH 10 mH 6 mH The time constant of an LR circuit represents the time in which the current in the circuit: Reaches 63.2% of its maximum value Reaches 50% of its maximum value Falls to 36.8% of its maximum value Reaches its maximum value Two inductors of 10 H and 20 H are connected in parallel. The equivalent inductance is: 6.67 H 30 H 15 H 10 H Two coils of self-inductances L 1 and L 2 are placed so close that the entire flux of one is linked with the other. The mutual inductance M between them is: L 1 L 2 L 1 L 2 (L 1 + L 2)/2 L 1/L 2 A choke coil has: High inductance and low resistance Low inductance and high resistance High inductance and high resistance Low inductance and low resistance If the current in an inductor is doubled, the energy stored in it will: Become four times Become double Become half Remain unchanged The core of a transformer is laminated to reduce: Eddy current loss Hysteresis loss Copper loss Flux leakage An inductor may store energy in: Its magnetic field Its electric field Its coils The core material only The self inductance L of a solenoid of length l and area of cross-section A , with a fixed number of turns N increases as: l decreases and A increases l and A both increase l and A both decrease l increases and A decreases An induction furnace works on the principle of: Eddy currents Self induction Mutual induction Peltier effect If the self-inductance of a coil is 2 mH and the current through it changes from 2 A to 8 A in 0.1 s, the induced emf is: 0.12 V 1.2 V 12 V 0.012 V Eddy currents are produced when: A metal is kept in a varying magnetic field A metal is kept in a steady magnetic field A circular coil is placed in a magnetic field Current is passed through a solenoid Which of the following is responsible for the 'damping' of oscillations in a real LCR circuit? Resistance R Inductance L Capacitance C Source Frequency A choke coil is used as a resistance in: AC circuits only DC circuits only Both AC and DC circuits Neither AC nor DC circuits The core of a transformer is laminated to minimize: Eddy current loss Hysteresis loss Copper loss Flux leakage The power factor of an ideal choke coil is: Zero One 0.5 Infinite Two coils are placed near each other. The mutual inductance between them does NOT depend on: The current flowing through the coils The number of turns in the coils The geometry of the coils The relative orientation of the coils A metal plate is swinging like a pendulum between the pole pieces of a strong magnet. It comes to rest quickly due to: Eddy currents Electromagnetic waves Electrostatic induction Hysteresis loss If the number of turns per unit length of a coil of a solenoid is doubled, the self-inductance of the solenoid will: Become four times Be doubled Be halved Remain unchanged The energy required to establish a steady current of 5 A in an inductor of self-inductance 2 H is: 25 J 10 J 50 J 5 J The current in a coil changes from 4 A to 0 A in 0.1 s. If the self-inductance of the coil is 2 H, the induced emf is: 80 V 40 V 20 V 0.8 V Which of the following is responsible for the energy loss in a transformer due to the reversal of magnetization in the core? Hysteresis loss Eddy current loss Copper loss Flux leakage A choke coil is used to limit the current in an AC circuit instead of a resistor because: It consumes almost zero power It increases the power factor It is cheaper than a resistor It converts AC to DC A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C , the frequency will be:- f 4 8f f 2 2 f 2 What is the value of inductance L for which the current is maximum in a series LCR circuit with C = 10 , F and = 1000 , s -1 1 mH cannot be calculated unless R is known 10mH 100mH The magnetic flux linked with a coil of N turns is . If the current through it is I , then the self-inductance is: N / I / I NI / I / (N ) 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 :- 300 V, 15A 450 V, 15A 450V, 13.5A 600V, 15A A small signal voltage V(t) = V 0 t is applied across an ideal capacitor C :- Current I(t), lags voltage V(t) by 90°. Over a full cycle the capacitor C does not consume any energy from the voltage source. Current I(t) is in phase with voltage V(t). Current I(t) leads voltage V(t) by 180°. A bulb connected in series with an air-cored solenoid is lit an a.c source. If a soft iron core is introduced in the solenoid The bulb stops glowing The bulb will glow brighter There is no change in glow of bulb The bulb will become dimmer A 40 F capacitor is connected to a 200 V , 50 Hz ac supply. The rms value of the current in the circuit is, nearly : 2.05 A 2.5 A 25.1 A 1.7 A A capacitor of capacitance 'C', is connected across an ac source of voltage V , given by V = V 0 t The displacement current between the plates of the capacitor, would then be given by I d = V 0 C t I d = V 0 C t I d =V 0 C t I d =V 0 C t 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? 0.4 A 2 A 4 A 0.2 A The peak voltage of the ac source is equal to The rms value of the ac source 2 times the rms value of the ac source 1/ 2 times the rms value of the ac source The value of voltage supplied to the circuit A 12 V, 60 W lamp is connected to the secondary of a step-down transformer, whose primary is connected to ac mains of 220 V. Assuming the transformer to be ideal, what is the current in the primary winding? 0.27 A 2.7 A 3.7 A 0.37 A An ac source is connected to a capacitor C . Due to decrease in its operating frequency Capacitive reactance decreases Displacement current increases Displacement current decreases Capacitive reactance remains constant In an ideal transformer, the turns ratio is N P N S = 1 2 . The ratio V S : V P is equal to (the symbols carry their usual meaning) : 1 : 2 2 : 1 1 : 1 1 : 4 The coefficient of self-induction of a solenoid is 0.18 mH. If a core of soft iron of relative permeability 900 is inserted, the self-inductance becomes: 162 mH 0.18 mH 0.0002 mH 900 mH An ac circuit contains a resistance of 1 k , a capacitor of 0.1 F and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately: 15.9 kHz 20.7 kHz 10.1 kHz 13.5 kHz The peak value of an alternating current is 5 A and frequency is 60 Hz. How long will the current, starting from zero, take to reach the peak value ? 1 120 s 1 240 s 1 30 s 1 60 s A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when: An iron rod is inserted in the coil Frequency of the AC source decreases Number of turns in the coil is reduced A capacitance of reactance X C = X L is included in the circuit The work done in increasing the current through an inductor from 0 to I is W . The work done in increasing the current from I to 2I is: 3W W 2W 4W The current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V is induced, the self-inductance of the circuit is: 4 H 2 H 0.4 H 0.2 H 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 H 4 H 3 H 2 H What is the value of the current through the inductor L in the circuit shown, a long time after the switch S is closed? (Assume the battery has emf E and no internal resistance, and inductor has zero resistance). E/R 1 E/(R 1 + R 2) Zero Infinity Two coils have a mutual inductance of 0.005 H. The current changes in the first coil according to equation I = I 0 t , where I 0 = 10 A and = 100 rad/s. The maximum value of induced emf in the second coil is: 5 V 2 V 10 V 0.5 V A long solenoid has n turns per unit length and radius r . A second shorter solenoid of N turns and radius R ( R > r ) is placed coaxially around the first solenoid. The mutual inductance of the pair is: 0 n N r 2 0 n N R 2 0 N 2 r 2 0 n 2 R 2 A coil of wire of certain radius has 100 turns and a self-inductance of 15 mH. The self-inductance of a second similar coil of 500 turns will be: 375 mH 75 mH 150 mH 30 mH Which of the following does NOT result in the production of eddy currents? A steady current flowing through a copper wire A metal block moving in a non-uniform magnetic field A changing magnetic flux through a solid metal plate A metal core inside a primary coil of an AC transformer Two coaxial circular loops of radii R and r ( R r ) are placed with their centres coinciding. The mutual inductance M between them is proportional to: r 2 / R R 2 / r r / R R / r 2 The self-inductance of a coil is L . If the number of turns is doubled without changing the length and area of the coil, the new self-inductance will be: 4L 2L L/2 L/4 The self-inductance L of a toroid of mean radius r , cross-sectional area A and total number of turns N is given by: 0 N 2 A 2 r 0 N A 2 r 0 N 2 A r 0 N A r 2 Two square loops, one of side L and another of side l ( L l ), are coplanar and their centers coincide. The mutual inductance M between them is proportional to: l 2 / L l / L L 2 / l l 2 / L 2 The magnetic energy density u B inside a solenoid of n turns per unit length carrying current I is: 1 2 0 n 2 I 2 0 n 2 I 2 1 2 0 n I 2 1 2 0 2 n 2 I 2 A light bulb is connected in series with an inductor and an AC source. When an iron core is inserted into the inductor, the brightness of the bulb: Decreases Increases Remains the same First increases then decreases Two coaxial solenoids are made such that the inner one has radius r 1 , number of turns N 1 and the outer one has radius r 2 , number of turns N 2 . Both have length l . The mutual inductance M is: 0 N 1 N 2 r 1 2 / l 0 N 1 N 2 r 2 2 / l 0 N 1 N 2 / l 0 (N 1 N 2) 2 r 1 2 / l The core of a transformer is laminated to reduce eddy currents. This is because lamination: Increases the resistance of the path of eddy currents Increases the magnetic flux Decreases the resistance of the core Decreases the hysteresis loss A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn is 4 10 -3 Wb. The self-inductance of the solenoid is: 1.0 H 0.4 H 2.5 H 2.0 H The current in a coil is changed from 5 A to 10 A in 10 -2 s and an induced emf of 50 V is produced. The energy stored in the magnetic field of the coil when the current is 10 A is: 5.0 J 0.5 J 1.0 J 2.5 J Which of the following serves as the best core for a transformer to minimize hysteresis loss? Soft iron Steel Copper Aluminium The physical quantity having the same unit as that of L/C is: Resistance Frequency Conductance Time A long solenoid has 1000 turns per metre. When a current of 2.0 A flows through it, the magnetic flux linked with each turn of the solenoid is 2 10 -3 Wb. The self-inductance of the solenoid of length 1 m is: 2.0 H 4.0 H 1.0 H 0.5 H An inductor of self-inductance L is connected in series with a bulb B and an AC source. The brightness of the bulb decreases when an iron rod is inserted into the inductor. This happens because: The reactance of the inductor increases The resistance of the inductor increases The voltage of the source decreases The reactance of the inductor decreases Which of the following quantity has dimensions of [ML 2T -2 A -1 ] ? Magnetic flux Self inductance Mutual inductance Magnetic field In a circuit L, C and R are connected in series with an alternating voltage source of frequency f . The current leads the voltage by 45 . The value of C is - 1 2 f(2 fL-R) 1 2 f(2 fL+R) 1 f(2 fL-R) 1 f(2 fL+R) A coil of inductive reactance 31 has a resistance of 8 . It is placed in series with a condenser of capacity reactance 25 . The combination is connected to an a.c. source of 110 volt. The power factor of the circuit is:- 0.56 0.64 0.80 0.33 Power dissipated in an LCR series circuit connected to an a.c. source of emf is : 2R ,/ , R 2+ (L - 1 C ) 2 2R ,/ , [R 2+ (L - 1 C ) 2 ] 2 [R 2+ (L - 1 C ) 2 ] ,/ ,R 2 [R 2+ (L - 1 C ) 2 ] ,/ ,R A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when Frequency of the AC source is decreased Number of turns in the coil is reduced A capacitance of reactance X C = X L is included in the same circuit An iron rod is inserted in the coil An inductor 20 mH, a capacitor 50 F and a resistor 40 are connected in series across a source of emf V = 10 340 t . The power loss in A.C. circuit is :- 0.51 W 0.67 W 0.76 W 0.89 W An inductor 20 mH, a capacitor 100 μF and a resistor 50 Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is 2.74 W 0.43 W 0.79 W 1.13 W An inductor of 10 mH and a resistor of 5 are connected in series to a 10 V battery. The time taken for the current to reach 63.2 % of its steady state value is: 2 ms 0.5 ms 5 ms 1 ms 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 3 . If instead C is removed from the circuit, the phase difference is again 3 between current and voltage. The power factor of the circuit is : 0.5 1.0 -1.0 zero 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 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10 2 A. The impedance of the circuit is 5 2 4 5 4 2 A series LCR circuit containing 5.0 H inductor, 80 F 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 50 rad/s and 25 rad/s 46 rad/s and 54 rad/s 42 rad/s and 58 rad/s 25 rad/s and 75 rad/s A series LCR circuit with inductance 10 H , capacitance 10 F , resistance 50 is connected to an ac source of voltage, V = 200 (100t) volt. If the resonant frequency of the LCR circuit is 0 and the frequency of the ac source is , then 0 = = 50 Hz 0 = 50 Hz , = 50 Hz = 100 Hz ; 0 = 100 Hz 0 = = 50 Hz In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 F and resistance R is 100 . The frequency at which resonance occurs is 15.9 rad/s 15.9 kHz 1.59 rad/s 1.59 kHz The net impedance of circuit (as shown in figure) will be 10 2 15 5 5 25 A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates: There is no current Displacement current of magnitude equal to I flows in the same direction as I Displacement current of magnitude equal to I flows in a direction opposite to that of I Displacement current of magnitude greater than I flows but can be in any direction A 10 F capacitor is connected to a 210 V, 50 Hz source as shown in figure. The peak current in the circuit is nearly ( = 3.14 ): 0.58 A 0.93 A 1.20 A 0.35 A To an ac power supply of 220 V at 50 Hz, a resistor of 20 , a capacitor of reactance 25 and an inductor of reactance 45 are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively 15.6 A and 45° 7.8 A and 30° 7.8 A and 45° 15.6 A and 30° A long solenoid of radius 2 cm and 1000 turns per metre has a small coil of 10 turns and radius 1 cm placed inside the solenoid co-axially. If the current in the solenoid changes from 0 to 2 A in 0.05 s, the induced emf in the small coil is: 1.58 10 -4 V 3.16 10 -4 V 7.9 10 -5 V 6.32 10 -4 V The unit of mutual inductance is Henry, which is equivalent to: Volt-second/Ampere Volt-Ampere/second Ampere-second/Volt Volt/Ampere A long solenoid of diameter 0.1 m has 2 10 4 turns per meter. At the center 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 from 4 A to 0 A in 0.05 s. The total induced emf in the coil is: 32 10 -4 V 16 10 -4 V 64 10 -4 V 8 10 -4 V A long solenoid of diameter 0.1 m has 2 10 4 turns per meter. 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. If the current in the solenoid changes at a constant rate from 0 A to 4 A in 0.05 s, the induced emf in the coil is: 6.3 mV 6.3 V 3.2 mV 3.2 V A long straight wire carries a current I . A square loop of side a is placed in the same plane at a distance a from the wire. The mutual inductance between them is: 0 a 2 2 0 a 2 0 a 4 2 0 2 a The current in an LR circuit builds up to 3/4 of its steady-state value in 4 seconds. The time constant of the circuit is (take 4 1.386 ): 2.88 s 4.00 s 1.38 s 5.76 s A rectangular loop of sides a and b is placed with its longer side b parallel to a long straight wire carrying current I . The distance between the wire and the nearer side of the loop is d . The mutual inductance of the system is: 0 b 2 ( d+a d ) 0 a 2 ( d+b d ) 0 ab 2 d 0 b 2 a d A long solenoid of diameter 0.1 m has 2 10 4 turns per meter. A coil of 100 turns and radius 0.01 m is placed inside at its center. What is the mutual inductance between them? 7.89 10 -4 H 2.5 10 -4 H 1.25 10 -3 H 3.14 10 -4 H The current in a coil of self-inductance 2.0 H is increasing as i = 2 (t 2) . The induced emf at t = 1 s is: -8 (1) V -4 (1) V -2 (1) V -4 (1) V Two identical inductors are connected in two different configurations P and Q , where a time varying current I(t) is flowing, as shown in the figure. The induced emf between points a and b for configuration P is E P and that for configuration Q is E Q . The ratio E P/E Q is: [Neglect the effect of mutual inductance.] 1 4 1 2 1 2 Consider a long solenoid of length l and radius r . If n is the number of turns per unit length and 0 is the permeability of free space, the inductance of the solenoid is: 0 r 2 n 2 l 0 n 2 r 2 l ( 0 2 )n 2 r 2 l 2 0 n 2 r 2 l