Practice Questions

Q13.A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ, an inductor of inductive reactance XL = 250π Ω and an unknown capacitor. The value of capacitance to maximise the average power should be: (take π2 = 10) (1) 400 μF (2) 4 μF (3) 40 μF (4) 25 μF

Q13.Consider the combination of two capacitors C1 and C2 , with C2 > C1 , when connected in parallel, the equivalent capacitance is 10 times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, C2 . C1 (1) 4 + √15 (2) 2 + √15 (3) 9 (4) 154

Q13.Two ions of masses 4 amu and 16 amu have charges +2 e and +3 e respectively. These ions pass through the region of the constant perpendicular magnetic field. The kinetic energy of both ions is the same. Then: (1) lighter ion will be deflected less than heavier ion (2) lighter ion will be deflected more than heavier ion (3) both ions will be deflected equally (4) no ion will be deflected

Q13.A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let rd and rα be their respective radii of circular path. The value of rdrα is equal to: (1) 1 (2) √2 √2 (3) 1 (4) 2

Q13.A particle is making simple harmonic motion along the X -axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 , respectively. The time period of its oscillation is given as: (1) 2+x21 (2) 2+x21 T = T = 2π√x2v21−v22 2π√x2v21+v22 (3) 2−x21 (4) 2−x21 T = T = 2π√x2v21+v22 2π√x2v21−v22

Q13.Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be: (1) 1: 2 (2) 1: 4 (3) 4: 1 (4) 2: 1

Q13.The current (i) at time t = 0 and t = ∞ respectively for the given circuit is : (1) 5E 18 , 18E55 (2) 5E18 , 10E33 (3) 10E 33 , 5E18 (4) 18E55 , 5E18

Q13.An L. C. R. circuit contains resistance of 110 Ω and a supply of 220 V at 300 rad s−1 angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45°. If on the other hand, the only the inductor is removed the current leads by 45° with the applied voltage. The R. M. S. current flowing in the circuit will be: (1) 2. 5 A (2) 2 A (3) 1 A (4) 1. 5 A

Q13.A ray of laser of a wavelength 630 nm is incident at an angle of 30° at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2 . 42 and that of air is 1. Choose the correct option. (1) Angle of refraction is 24 . 41°. (2) Angle of refraction is 30°. (3) Refraction is not possible. (4) Angle of refraction is 53 . 4°.

Q13.Two resistors 𝑅1 = ( 4 ± 0 . 8 ) Ω and 𝑅2 = ( 4 ± 0 . 4 ) Ω are connected in parallel. The equivalent resistance of their parallel combination will be : (1) ( 4 ± 0 . 4 ) Ω (2) ( 2 ± 0 . 4 ) Ω (3) ( 4 ± 0 . 3 ) Ω (4) ( 2 ± 0 . 3 ) Ω

Q13.A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of 18 cm from the center of the magnet. If BH = 0. 4 G, the magnetic moment of the magnet is (1 G = 10−4 T) (1) 2. 880 × 103 J T−1 (2) 2. 880 × 102 J T−1 (3) 2. 880 J T−1 (4) 28. 80 J T−1

Q13.A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5 A. The magnetic flux density produced by the solenoid is: (Permeability of free space = 4π × 10−7 H m−1 ) (1) (π) T (2) (2 × 10−3π) T (3) ( π5 ) T (4) (10−4π) T

Q13.The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15Ω resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 V is maintained across AC. JEE Main 2021 (17 Mar Shift 2) JEE Main Previous Year Paper (1) 2. 44μA (2) 2. 44 mA (3) 4. 87 mA (4) 4. 87μA

Q13.A plane electromagnetic wave of frequency 100 MHz is traveling in a vacuum along the x−direction. At a → → particular point in space and time, B = 2. 0 × 10−8 ˆkT⋅ (where, ˆk is unit vector along z−direction) What is E at this point? (1) 0. 6ˆj V m−1 (2) 6. 0ˆk V m−1 (3) 6. 0ˆj V m−1 (4) 0. 6ˆk V m−1

Q13.A proton and an α-particle, having kinetic energies Kp and Kα , respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of α -particle is 2 : 1. The ratio of Kp : Kα is: (1) 1 : 8 (2) 8 : 1 (3) 1 : 4 (4) 4 : 1

Q13.The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is: (1) (7500 ± 375)Ω (2) (5700 ± 285)Ω (3) (7500 ± 755)Ω (4) (5700 ± 375)Ω

Q14.The resistance of a conductor at 15°C is 16 Ω and at 100°C is 20 Ω. What will be the temperature coefficient of resistance of the conductor? (1) 0. 010°C−1 (2) 0. 033°C−1 (3) 0. 003°C−1 (4) 0. 042°C−1

Q14.The angular frequency of alternating current in a L-C-R circuit is 100 rad s−1 . The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser. (1) 1. 33 H and 150 μF (2) 0. 8 H and 150 μF (3) 1. 33 H and 250 μF (4) 0. 8 H and 250 μF

Q14.An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8 A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit (in s). (1) 0. 4 (2) 0. 2 (3) 0. 125 (4) 0. 8

Q14.Match List-I with List-II. List - I List - II (a) ωL > ωC1 (i) Current is in phase with emf (b) ωL = ωC1 (ii) Current lags behind the applied emf (c) ωL < ωC1 (iii) Maximum current occurs (d) Resonant frequency (iv) Current leads the emf Choose the correct answer from the options given below. (1) (a) - (ii) ; (b) - (i) ; (c) - (iv) ; (d) - (iii) (2) (a) - (ii) ; (b) - (i) ; (c) - (iii) ; (d) - (iv) (3) (a) - (iii) ; (b) - (i) ; (c) - (iv); (d) - (ii) (4) (a) - (iv) ; (b) - (iii) ; (c) - (ii); (d) - (i)

Q14.A current of 1 . 5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is : (Assume that the current is flowing in the clockwise direction.) (1) 2√3 × 10-5 T, inside the plane of triangle (2) 2√3 × 10-7 T, outside the plane of triangle (3) 3 × 10-7 T, outside the plane of triangle (4) 3 × 10-5 T, inside the plane of triangle

Q14.The given potentiometer has its wire of resistance 10 Ω. When the sliding contact is in the middle of the potentiometer wire, the potential drop across 2 Ω resistor is: (1) 10 V (2) 5 V (3) 40 9 V (4) 4011 V

Q14.A current through a wire depends on time as 𝑖= 𝛼0𝑡+ 𝛽𝑡2, where 𝛼0 = 20 A s-1 and 𝛽= 8 A s-2. Find the charge crossed through a section of the wire in 15 s . (1) 2250 C (2) 11250 C (3) 2100 C (4) 260 C

Q14.In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given the area of the plate = A ) (1) 15 Kε0 A (2) 15 Kε0 A 34 d 6 d (3) 25 Kε0 A (4) 9 Kε0 A 6 d 6 d

Q14.In an ac circuit, an inductor, a capacitor and a resistor are connected in series with XL = R = XC. Impedance of this circuit is : (1) Zero (2) R (3) R√2 (4) 2R2 JEE Main 2021 (31 Aug Shift 1) JEE Main Previous Year Paper