The resistance of the tungsten wire in the light bulb, which is 120V/75 W and powered by a 120 V direct current supply, is

• 0.37 Ω

• 1.2 Ω

• 2.66 Ω

• 192 Ω

The value of the current I₁, I₂ and I₃ flowing through the circuit given below is

• I₁ = − 3A, I₂ = 2A, I₃ = − 1A

• I₁ = 2A, I₂ = − 3A, I₃ = − 1A

• I₁ = 3A, I₂ = − 1A, I₃ = − 2A

• I₁ = 1A, I₂ = − 3A, I₃ = − 2A

A silver wire has temperature coefficient of resistivity 4 x 10^-3 / °C and its resistance at 20°C is 10 Ω. Neglecting any change in dimensions due to the change in temperature, its resistance at 40°C is

• 0.8 Ω

• 1.8 Ω

• 9.2 Ω

• 10.8 Ω

A charge Q placed at the centre of a metallic spherical shell with inner and outer radii R₁ and R₂ respectively. The normal component of the electric field at any point on the Gaussian surface with radius between R₁ and R₂ will be

• Zero

• $\frac{\mathrm{Q}}{4{{\mathrm{\pi R}}_1}^2}$

• $\frac{\mathrm{Q}}{4{{\mathrm{\pi R}}_2}^2}$

• $\frac{\mathrm{Q}}{4\mathrm{\pi } ({\mathrm{R}}_1 - {\mathrm{R}}_2{)}^2}$

45.

A sphere of radius R has a uniform volume charge density ρ. The magnitude of electric field at a distance r from the centre of the sphere, where r > R, is

• $\frac{\mathrm{\rho }}{4{\mathrm{\pi \epsilon }}_0{\mathrm{r}}^2}$

• $\frac{{\mathrm{\rho R}}^2}{{\mathrm{\epsilon }}_0{\mathrm{r}}^2}$

• $\frac{{\mathrm{\rho R}}^3}{{\mathrm{\epsilon }}_0{\mathrm{r}}^2}$

• $\frac{{\mathrm{\rho R}}^3}{3{\mathrm{\epsilon }}_0{\mathrm{r}}^2}$

Five equal point charges with Q = 10 nC are located at x = 2, 4, 5, 1 O and 20 m. If ε₀ = [10^-9 / 36π] F/m, then the potential at the origin (x = O) is

• 9.9 V

• 11.1 V

• 90 V

• 99 V

Two infinitely long parallel plates of equal areas 6 cm² are separated by a distance of 1 cm. While one of the plates has a charge of + 10 nC and the other has − 10 nC. The magnitude of the electric field between the plates, if ${\mathrm{\epsilon }}_0 = \frac{{10}^{-9}}{36\mathrm{\pi }}$ F/m is

• 0.6 π kV/m

• 6 π kV/m

• 600 π kV/m

• 60 π V/m

A proton moves with a speed of 5.0 x 10⁶ m/s along the x-axis. It enters a region where there is a magnetic field of magnitude 2.0 Tesla directed at an angle of 30° to the
x-axis and lying in the xy-plane. The magnitude of the magnetic force on the proton is

• 0.8 × 10^-13 N

• 1.6 × 10^-13 N

• 8.0 × 10^-13 N

• 8.01 × 10^-13 N

A long straight wire of radius R carries a steady current I₀, uniformly distributed throughout the cross-section of the wire. The magnetic field at a radial distance r from the centre of the wire, in the region r > R, is

• $\frac{{\mathrm{\mu }}_0{\mathrm{I}}_0}{2\mathrm{\pi r}}$

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

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

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

If the cyclotron oscillator frequency is 16 MHz, then what should be the operating magnetic field for accelerating the proton of mass 1.67 x 10^-27 kg ?

• 0.334 πT

• 3.34 πT

• 33.4 πT

• 334 πT