Practice Questions

Q18.Drift speed of electrons, when 1.5 A current flows in a copper wire of cross section 5 mm2 is 𝑣𝑑. If the electron density in copper is 9 × 1028 m-3 the value of 𝑣𝑑 in mm 𝑠-1 is close to (Take charge of an electron to be = 1.6 × 10-19 C) (1) 0.2 (2) 3 (3) 2 (4) 0.02

Q18.In the circuit shown, a four-wire potentiometer is made of a 400 cm long wire, which extends between A and B . The resistance per unit length of the potentiometer wire is r = 0.01 Ω / cm . If an ideal voltmeter is JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper connected as shown with jockey J at 50 cm from end A , the expected reading of the voltmeter will be: (1) 0.50 V (2) 0.25 V (3) 0.75 V (4) 0.20 V

Q18.A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is (1) 560 pJ (2) 600 pJ (3) 508 pJ (4) 692 pJ

Q18.The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0 −0.5 A? (1) 0.2 ohm (2) 0.5 ohm (3) 0.002 ohm (4) 0.02 ohm

Q18.A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E , as shown in figure. Its bob has mass m and charge q . The time period of the pendulum is given by: L L (1) 2π (2) 2π qE qE 2 √ g + m √ √g2 + m (3) 2π LqE (4) 2π L 2 √ g - m √ √g2 - q2Em2

Q18.Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P1 and P2 respectively, then: (1) P1 = 4 W, P2 = 16 W (2) P1 = 9 W, P2 = 16 W (3) P1 = 16 W, P2 = 9 W (4) P1 = 16 W, P2 = 4 W

Q19.Determine the charge on the capacitor in the following circuit: (1) 2 μC (2) 60 μC (3) 10 μC (4) 200 μC

Q19.In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V . Calculate the radius of the path if a magnetic field 100mT is then applied. [Charge of the electron = 1.6 × 10−19C Mass of the electron = 9.1 × 10−31 kg] (1) 7.5 × 10−3 m (2) 7.5 × 10−2 m (3) 7.5 m (4) 7.5 × 10−4 m

Q19.Two wires A & B are carrying currents I1 and I2 as shown in the figure. The separation between them is d . A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are: (1) x = ± and x = I2 d (I1−I2) (I1−I2) I1d (2) x = ( I1+I2I1 )d (3) x = ( I1+I2I2 )d and x = ( I1−I2I2 )d (4) x = ( I1−I2I1 )d and x = (I1+I2)I2 d

Q19.A circular coil having N turns and radius r carries a current I . It is held in the XZ plane in a magnetic field B^i . The torque on the coil due to the magnetic field is: (1) Bπr2IN (2) Br2I (3) Bπr2I (4) Zero πN N

Q19.A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 × 10−6 J/T when a magnetic intensity of 60 × 103 A/m is applied. Its magnetic susceptibility is: JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper (1) 3.3 × 10−2 (2) 4.3 × 10−2 (3) 2.3 × 10−2 (4) 3.3 × 10−4 →

Q19.In free space, a particle 𝐴 of charge 1 μC is held fixed at point 𝑃 . Another particle 𝐵 of the same charge and mass 4 μg is kept at a distance of 1 mm from 𝑃. If 𝐵 is released, then its velocity at a distance of 9 mm from 𝑃 is: [Take 1 = 9 × 109 N m2 C-2 ] 4πϵ0 (1) 1.0 m s-1 (2) 1.5 × 102 m s-1 (3) 2.0 × 103 m s-1 (4) 3.0 × 104 m s-1

Q19.The resistive network shown below is connected to a D . C . source of 16 V . The power consumed by the network is 4 Watt. The value of R is: (1) 16 Ω (2) 8 Ω (3) 6 Ω (4) 1 Ω

Q19.In a conductor, if the number of conduction electrons per unit volume is 8.5 × 1028 m−3 and mean free time is 25 fs (femto second), it’s approximate resistivity is: (me = 9.1 × 10−31 kg) (1) 10−7 Ω m (2) 10−6 Ω m (3) 10−5 Ω m (4) 10−8 Ω m

Q19.A paramagnetic material has 1028 atoms m−3 . Its magnetic susceptibility at temperature 350 K is 2.8×10−4 . Its susceptibility at 300 K is (1) 3.726 x 10−4 (2) 2.672 x 10−4 (3) 3.267 x 10−4 (4) 3.672 x 10−4 JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

Q19.An electron, moving along the x− axis with an initial energy of 100 eV, enters a region of magnetic field → B = (1.5 × 10−3 T)ˆk at S (see figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is: (electron’s charge 1.6 × 10−19 C , mass of electron = 9.1 × 10−31 kg ) (1) 1.22 cm (2) 12.87 cm (3) 11.65 cm (4) 2.25 cm

Q19.A cell of internal resistance r drives current through an external resistance R . The power delivered by the cell to the external resistance will be maximum when: (1) R = 2r (2) R = r (3) R = 1000 r (4) R = 0.001 r

Q19.A 2 W carbon resistor is color coded with green, black, red and silver respectively. The maximum current which can be passed through this resistor is: (1) 100 mA (2) 0.4 mA (3) 20 mA (4) 63 mA

Q19.A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 × 10−19C ) (1) 9.1 × 10−31 kg (2) 1.6 × 10−27 kg (3) 2.0 × 10−24 kg (4) 1.6 × 10−19 kg

Q19.The actual value of resistance R , shown in the figure is 30Ω. This is measured in an experiment as shown using the standard formula R = VI , where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5% less, then the internal resistance of the voltmeter is: (1) 35Ω (2) 600Ω (3) 570Ω (4) 350Ω

Q19.Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an N-type semiconductor, the density of electrons is 1019 m-3 and their mobility is 1.6 m2 V-1 s-1, then the resistivity of the semiconductor (since it is an N-type semiconductor contribution of holes is ignored) is close to: (1) 0.2 Ω m (2) 4 Ω m (3) 2 Ω m (4) 0.4 Ω m

Q19.A proton and an α - particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2 ) are accelerated from rest through a potential difference V . If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp : rα of the circular paths described by them will be: (1) 1 : 3 (2) 1 : √2 (3) 1 : 2 (4) 1 : √3

Q20.There are two long co-axial solenoids of same length l. The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2 , respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is : (1) n1 (2) n2 ⋅r1 n2 n1 r2 n2 (3) n2 2 (4) ⋅r2 n1 n1 r21

Q20.Space between two concentric conducting spheres of radii a and b ( b > a ) is filled with a medium of resistivity ρ . The resistance between the two spheres will be: ρ 1 1 ρ 1 1 (1) + (2) + 4π a b 2π a b ρ 1 1 ρ 1 1 (3) - (4) - 4π a b 2π a b

Q20.The Wheatstone bridge shown in the figure below, gets balanced when the carbon resistor used as R1 has the colour code (orange, red, brown). The resistors R2 and R4 are 80 Ω and 40 Ω , respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as R3 , would be JEE Main 2019 (10 Jan Shift 2) JEE Main Previous Year Paper (1) brown, blue, black. (2) brown, blue, brown. (3) grey, black, brown. (4) red, green, brown.