A resistor is constructed as hollow cylinder of dimensions r_a = 0.5 cm and r_b = 1.0 cm and ρ = 3 .5 x-10^-5 Ωm. The resistance of the configuration for the length of 5 cm cylinder is 

• 7.42 × 10^-3 Ω

• 10.56 × 10^-3 Ω

• 14.38 × 10^-3 Ω

• 16.48 × 10^-3 Ω

The resistances are connected as shown in the figure below. Find the equivalent resistance between the points A and B.

• 205 Ω

• 10 Ω

• 3.5 Ω

• 5 Ω

The figure below shows a 2.0 V potentiometer used for the determination of internal resistance of a 2.5 V cell. The balance point of the cell in the open circuit is 75 cm. When a resistor of 10 Ω is used in the external circuit of the cell, the balance point shifts to 65 cm length of potentiometer wire. Then the internal resistance of the cell is

• 2.5 Ω

• 2.0 Ω

• 1.54 Ω

• 1.0 Ω

An electric heater boils 1 kg of water in a time t₁. Another heater boils the same amount of water in a time t₂. When the two heaters are connected in parallel, the time required by them together to boil the same amount of water is

• t₁ + t₂

• t₁t₂

• $\frac{{\mathrm{t}}_1{\mathrm{t}}_2}{{\mathrm{t}}_{1 }+ {\mathrm{t}}_2}$

• $\frac{{\mathrm{t}}_1 - {\mathrm{t}}_2}{2}$

Two thin metallic strips, carrying current in the direction shown, cross each other perpendicularly without touching but being close to each other, as shown in the figure. The regions which contain some points of zero magnetic induction are

• I and II

• I and III 

• I and IV

• II and III

The force on a conductor of length l placed in a magnetic field of magnitude B and carrying a current I is given by (θ is the angle, the conductor makes with the direction of B)

• F = I l B sin θ

• F = I² l B² sin θ

• F = I l B cos θ

• $\mathrm{F} = \frac{{\mathrm{I}}^2\mathrm{l}}{\mathrm{B}} \sin \mathrm{\theta }$

A needle made of bismuth is suspended freely in a magnetic field. The angle which the needle makes with the magnetic field is

• 0°

• 45°

• 90°

• 180°

48.

The resonant frequency of an LCR circuit occurs at a frequency equal to

• $\frac{1}{\mathrm{LC}}$

• $\frac{1}{\sqrt{\mathrm{LC}}}$

• $\frac{1}{\mathrm{LCR}}$

• $\frac{1}{\mathrm{CR}}$

An AC is given by i = i₁ cos ωt + i₂ sin ωt. The rrns current is given by

• $\frac{{\mathrm{i}}_1 + {\mathrm{i}}_2}{\sqrt{2}}$

• $\frac{{\mathrm{i}}_1 - {\mathrm{i}}_2}{\sqrt{2}}$

• $\sqrt{\left(\frac{{{\mathrm{i}}_1}^2 + {{\mathrm{i}}_2}^2}{2}\right)}$

• $\sqrt{\left(\frac{{{\mathrm{i}}_1}^2 - {{\mathrm{i}}_2}^2}{2}\right)}$

The coefficient of mutual inductance between the primary and secondary of the coil is 5 H. A current of 10 A is cut off in 0.5 s. The induced emf is 

• 1 V

• 10 V

• 5 V

• 100 V