List of practice Questions

The root mean square (RMS) value of an alternating voltage applied to a full-wave rectifier is \( \frac{V_0}{\sqrt{2}} \). Then the root mean square value of the rectified output voltage is:

A double-convex lens of power \( P \), with each face having the same radius of curvature, is cut along its principal axis. The two parts are arranged as shown in the figure. The power of the combination will be: \includegraphics[width=0.3\linewidth]{14image.png}

State any two properties of a nucleus.

Write the drawbacks of Rutherford’s atomic model. How did Bohr remove them? Show that different orbits in Bohr’s atom are not equally spaced.

(i) Why do long-distance radio broadcasts use short-wave bands?
(ii) Why are optical and radio telescopes built on the ground, but X-ray astronomy is possible only from satellites orbiting the Earth?

An inductor, a capacitor, and a resistor are connected in series with an AC source \( v = v_m \sin \omega t \). Derive an expression for the average power dissipated in the circuit. Also, obtain the expression for the resonant frequency of the circuit.

A proton with kinetic energy $1.3384 \times 10^{-14 \, \text{J}$ moving horizontally from north to south, enters a uniform magnetic field $B = 2.0 \, \text{mT}$ directed eastward. Calculate:}
\textbf{(a) the speed of the proton,

Define ‘current density’. Is it a scalar or a vector? An electric field $\vec{E$ is maintained in a metallic conductor. If $n$ be the number of electrons (mass $m$, charge $-e$) per unit volume in the conductor and $\tau$ its relaxation time, show that the current density $\vec{j} = \alpha \vec{E}$, where $\alpha = \left( \frac{ne^2}{m} \right) \tau$.}

A cube of side $0.1 \, \text{m$ is placed, as shown in the figure, in a region where electric field $\vec{E} = 500x \, \hat{i}$ exists. Here $x$ is in meters and $E$ in $\text{N/C}$. Calculate:}
\textbf{(a) the flux passing through the cube, and

Plot a graph showing the variation of current with voltage for the material GaAs. On the graph, mark the region where: \textbf{(a) resistance is negative, and

Consider a neutron (mass $m$) of kinetic energy $E$ and a photon of the same energy. Let $\lambda_n$ and $\lambda_p$ be the de Broglie wavelength of the neutron and the wavelength of the photon, respectively. Obtain an expression for $\frac{\lambda_n{\lambda_p}$.}

A plano-convex lens of focal length $16 \, \text{cm$ is made of a material of refractive index $1.4$. Calculate the radius of the curved surface of the lens.}

Monochromatic light of frequency $5.0 \times 10^{14 \, \text{Hz}$ passes from air into a medium of refractive index $1.5$. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media.}

Assertion (A): Plane and convex mirrors cannot produce real images under any circumstance.
Reason (R): A virtual image cannot serve as an object to produce a real image.

Assertion (A): Two long parallel wires, freely suspended and connected in series to a battery, move apart.
Reason (R):Two wires carrying current in opposite directions repel each other.

Assertion (A): The mutual inductance between two coils is maximum when the coils are wound on each other.
Reason (R): The flux linkage between two coils is maximum when they are wound on each other.

Assertion (A): In photoelectric effect, the kinetic energy of the emitted photoelectrons increases with increase in the intensity of the incident light.
Reason (R): Photoelectric current depends on the wavelength of the incident light.

Ge is doped with As. Due to doping:}