Video Lecture
Theory For Making Notes
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Practice Questions (Basic Level)
Q.1
The mutual inductance between a pair of coils each of N turns is M. If a current i in the first coil is brought to zero in time t, then, average emf induced in the second coil is
(a) \frac{{Mi}}{t}
(b) \frac{{NMi}}{t}
(c) \frac{{Mi}}{{Nt}}
(d) \frac{{Mt}}{{iN}}
Ans. (a)
Q.2
Two coils X and Y are placed in a circuit such that a current changes by 2 A in coil X and the magnetic flux change of 0.4 weber occur in Y. The value of mutual inductance of the coils is
(a) 0.2 henry
(b) 5 henry
(c) 0.8 henry
(d) 2 henry
Ans. (a)
Q.3
If two coils of self inductance 4H and 16H are wound on the same iron core. The coefficient of mutual inductance for them will be
(a) 8H (b) 10H (c) 20H (d) 164H
Ans. (a)
Q.4
A small square loop of wire of side l is placed inside a large square loop of wire of side
L( L >> l). The loops are co-planar and their centres coincide. The mutual inductance of the system is proportional to
(a) l/L (b) l2/L (c) L/l (d) L2/l
Ans. (b)
5.
An ideal transformer has 500 and 5000 turns in primary and secondary winding respectively. If the primary voltage is connected to a 6 V battery then the secondary voltage is
(a) 0
(b) 60 V
(c) 0.6 V
(d) 6.0 V
Ans (a)
6.
A step-down transformer transforms a supply line voltage of 2200 volt into 220 volt. The primary coil has 5000 turns. The number of turns in the secondary are
(a) 5000
(b) 550
(c) 500
(d) 450
Ans (b)
7.
A transformer
(a) transforms energy
(b) transforms frequency
(c) transforms voltage
(d) generates e.m.f.
Ans (c)
8.
In a transformer, the number of turns of primary coil and secondary coil are 5 and 4 respectively. If 240 V is applied on the primary coil, then the ratio of current in primary and secondary coil is
(a) 4 : 5
(b) 5 : 4
(c) 5 : 9
(d) 9 : 5
Ans (A)
9.
The number of turns in the primary and secondary turns of a transformer are 1000 and 3000 respectively. If 80 V AC is supplied to the primary coil of the transformer, then the potential difference per turn of the secondary coil would be
(a) 240 V
(b) 2400 V
(c) 0.24 V
(d) 0.08 V
Ans (d)
10.
A transformer has 200 windings in the primary and 400 windings in the secondary. The primary is connected to an ac supply of 110 V a current of 10 A flows in it. The voltage across the secondary and the current in it, respectively, are
(a) 55V, 20 A
(b) 440 V, 5A
(c) 220 V, 10A
(d) 220V, 5A
Ans (d)
Practice Questions (JEE Main Level)
Q.1
The diagram shows a solenoid carrying time varying current I={{I}_{0}}t. On the axis of this solenoid a ring has been placed. The mutual inductance of the ring and the solenoid is M and the self inductance of the ring is L. If the resistance of the ring is R then maximum current which can flow through the ring is
(a) \frac{{\left( {2M+L} \right){{I}_{0}}}}{R}
(b) \frac{{M{{I}_{0}}}}{R}
(c) \frac{{\left( {2M-L} \right){{I}_{0}}}}{R}
(d) \frac{{\left( {M+L} \right){{I}_{0}}}}{R}
Ans. (b)
Q.2
A dynamo dissipates 20 watt when it supplies a current of 4 amp through it. If the terminal potential difference is 220 volt, then the emf produced is
(a) 220V (b) 225V (c) 215V (d) 300V
Ans. (b)
Q.3
Two coils of inductances L1 and L2 are linked such that their mutual inductance is M
(a) M={{L}_{1}}+{{L}_{2}}
(b) M=\frac{1}{2}({{L}_{1}}+{{L}_{2}})
(c) The maximum value of M is (L1 + L2)
(d) The maximum value of M is \sqrt{{{{L}_{1}}{{L}_{2}}}}
Ans. (d)
Q.4
If turn ratio is 3 : 1 then V0 is equal to
(a) 5 V (b) 45 V (c) 15 V (d) 0
Ans. (d)
Q.5
A transformer has turn ratio 2 and input power 3600 W. Load current is 20 A. Efficiency . Find the internal resistance
(a) 9\,\Omega
(b) 1.9\,\Omega
(c) 1.2\,\Omega
(d) 0.9\,\Omega
Ans. (d)
Practice Questions (JEE Advance Level)
Q.1
A small square loop of wire of side l is placed inside a large square loop of wire of side L (>>l). The loops are coplanar and their centers coincide. The mutual inductance of the system must be
(a) 2\sqrt{2}\frac{{{{\mu }_{o}}{{l}^{2}}}}{{\pi {{L}^{2}}}}
(b) 2\sqrt{2}\frac{{{{\mu }_{o}}{{l}^{2}}}}{{\pi L}}
(c) 2\frac{{{{\mu }_{o}}{{l}^{2}}}}{{\pi L}}
(d) \frac{{{{\mu }_{o}}{{l}^{2}}}}{{\sqrt{2}\pi L}}
Ans : (b)
Q.2
A long solenoid having 200 turns per cm carries a current of 1.5 amp. At the center of it is placed a 100 turns of cross-sectional area 3.14 ´ 10-4 m2 having its axis parallel to the field produced by the solenoid. When the direction of current in the solenoid is reversed within 0.05 s, the emf induced in the coil must be
(a) 0.048A (b) 1.45A (c) 0.48A (d) 2.42A
Ans : (a)
Q.3
A current i = 33.6 (1 + 2t) mA increases at a steady rate in a long straight wire. A small circular loop of radius a = 10-3 m has its plane parallel to the wire and is placed at a distance of 1 m from the wire. The resistance of the loop is 8.4 ´ 10-4 W. The magnitude of induced current in the loop is \displaystyle k\times {{10}^{{-11}}}A. Where k is
(a) 2 (b) 3 (c) 5 (d) 8
Ans. (c)
Q.4
A very long conductor and an isosceles triangular conductor lie in a plane and separated from each other as shown in the figure. a = 10 cm; b = 20 cm; h = 10 cm
If current in the straight wire is increasing at a rate of 2 A/s, find the magnitude of current in the triangular wire. Diameter of the wire cross-section d = 1 mm. Resistivity of the wire, r = 1.8 ´ 10-8 Wm.
(a) 2 \displaystyle \mu A
(b) 1.67 \displaystyle \mu A
(c) 3.7 \displaystyle \mu A
(d) 2.2 \displaystyle \mu A
Ans. (d)
Q.5
A charge Q is uniformly distributed over a non-conducting ring of radius R. The ring is rotated clockwise from rest with a constant angular acceleration a. A conducting ring of radius ‘a’ is placed concentrically at the centre of the charged ring (a << R).
If resistance of the small ring is ‘r’, then the value of induced current in it must be
(a) \frac{{{{\mu }_{o}}Q{{a}^{2}}\alpha }}{{2Rr}}
(b) \frac{{3{{\mu }_{o}}Q{{a}^{2}}\alpha }}{{2Rr}}
(c) \displaystyle \frac{{{{\mu }_{o}}Qa\alpha }}{{4{{R}^{2}}r}}
(d) \frac{{{{\mu }_{o}}Q{{a}^{2}}\alpha }}{{4Rr}}
Ans. (d)
Q.6
A very small loop of radius a is placed at the centre of a very large loop of radius b as shown in the figure. The large loop carries a constant current Io and is kept fixed in space. The small loop is rotated about its diametric axis with angular velocity w. If the resistance of the small loop is R and the self inductance is negligible.
Find the torque required to rotate the small loop.
(a) {{\left[ {\frac{{{{\mu }_{o}}\pi {{b}^{2}}{{I}_{o}}\omega }}{{2a}}} \right]}^{2}}\,\left( {\frac{\omega }{R}} \right)\,{{\sin }^{2}}\omega t
(b) {{\left[ {\frac{{{{\mu }_{o}}\pi {{a}^{{}}}{{I}_{o}}\omega }}{{3{{b}^{3}}}}} \right]}^{2}}\,\left( {\frac{\omega }{R}} \right)\,{{\sin }^{2}}\omega t
(c) {{\left[ {\frac{{{{\mu }_{o}}\pi {{a}^{2}}{{I}_{o}}\omega }}{{2b}}} \right]}^{2}}\,\left( {\frac{\omega }{R}} \right)\,{{\sin }^{2}}\omega t
(d) {{\left[ {\frac{{{{\mu }_{o}}\pi {{a}^{2}}{{I}_{o}}\omega }}{{2b}}} \right]}^{2}}\,\,{{\sin }^{2}}\omega t
Ans. (c)
Comprehension ( Q.7 to Q.8)
An equilateral triangular frame PQR of mass M and side a is at rest is under the influence of horizontal magnetic field B and gravitational field as shown in the figure.
Q.7
Find the magnitude and direction of current in the frame so that the frame remains at rest.
(a) \frac{{Mg}}{{aB}}
(b) \frac{{2Mg}}{{aB}}
(c) \frac{{Mg}}{{2aB}}
(d) \frac{{Mg}}{{{{a}^{2}}B}}
Ans : (b)
Q.8
If the frame is slightly displaced in its plane perpendicular to PQ, show that its motion is simple harmonic and find its period of oscillation.
[Neglect EMF induced due to motion of the loop]
(a) \pi \sqrt{{\frac{{\sqrt{3}\,\,a}}{g}}}
(b) \pi \sqrt{{\frac{{3\,\,a}}{g}}}
(c) 2\pi \sqrt{{\frac{{\sqrt{3}\,\,a}}{g}}}
(d) \frac{\pi }{2}\sqrt{{\frac{{\sqrt{3}\,\,a}}{g}}}
Ans : (a)