Two copper wires have their masses in the ratio 2 : 3 and the lengths in the ratio 3 : 4.The ratio of their resistances is

• 4 : 9

• 27 : 32

• 16 : 9

• 27 : 128

Two different conductors have same resistance at 0°C. It is found that the resistance of the first conductor at t₁°C is equal to the resistance of the second conductor at t₂°C. The ratio of the temperature coefficients of resistance of the conductors, $\frac{{\mathrm{\alpha }}_1}{{\mathrm{\alpha }}_2}$ is

• $\frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}$

• $\frac{{\mathrm{t}}_2 - {\mathrm{t}}_1}{{\mathrm{t}}_2}$

• $\frac{{\mathrm{t}}_2 - {\mathrm{t}}_1}{{\mathrm{t}}_1}$

• $\frac{{\mathrm{t}}_2}{{\mathrm{t}}_1}$

In the given circuit diagram the current through the battery and the charge on the capacitor respectively in steady state are

• 1 A and 3 µC

• 17 A and 0 µC

• 11 A and 3 µC

• 6 A and 0 µC

A potentiometer wire of length 10 m and resistance 20 Ω is connected in series with a 15 V battery and an external resistance 40 Ω. A secondary cell of emf E in the secondary circuit is balanced by 240 cm long potentiometer wire. The emf E of the cell is

• 2.4 V

• 1.2 V

• 2.0 V

• 3 V

A current I enters a circular coil of radius R, branches into two parts and then recombines as shown in the circuit diagram

The resultant magnetic field at the centre of the coil is

• zero

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}$

• $\frac{3}{4} \left(\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}\right)$

• $\frac{1}{4} \left(\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}\right)$

The resistance of a galvanometer is 50 Ω and it shows full scale deflection for a current of 1 mA. To convert it into a voltmeter to measure 1 V and as well as 10 V (Refer circuit diagram) the resistances R₁ and R₂ respectively are

• 950 Ω and 9150 Ω

• 900 Ω and 9950 Ω

• 900 Ω and 9900 Ω

• 950 Ω and 9000 Ω

Two long parallel wires carry currents i₁ and i₂ such that i₁ >i₂. When the currents are in the same direction, the magnetic field at a point midway between the wires is 6 x 10^-6 T. If the direction of i₂ is reversed, the field becomes 3 x 10^-5 T. The ratio $\frac{{\mathrm{i}}_1}{{\mathrm{i}}_2}$ is

• $\frac{1}{2}$

• 2

• $\frac{2}{3}$

• $\frac{3}{2}$

A coil of 100 turns and area 2 x 10^-2 m², pivoted about a vertical diameter in a uniform magnetic field carries a current of 5A. When the coil is held with its plane in North-South direction, it experiences a torque of 0. 3 Nm. When the plane is in East-West direction the torque is 0.4 Nm. The value of magnetic induction is (Neglect earth's magnetic field)

• 0.2 T

• 0.3 T

• 0.05 T

• 0.1 T

The angle of dip at a place is 37° and the vertical component of the earth's magnetic field is 6 x 10^-5 T. The earth's magnetic field at this place is (tan 37° = 3/ 4)

• 7 × 10^-5 T

• 6 × 10^-5 T

• 5 × 10^-5 T

• 10^-4 T

50.

The impedance of a R-C circuit is Z₁ for frequency f and Z₂ for frequency 2f. Then Z₁/Z₂ is

• between 1 and 2

• 2

• 2 between $\frac{1}{2}$ and 1

• $\frac{1}{2}$