An inductor of inductance \(L\), a capacitor of capacitance \(C\) and a resistor of resistance \(R\) are connected in series to an AC source of potential difference \(V\) volts as shown in Figure. The potential difference across \(L\), \(C\) and \(R\) is \(40~\text{V}\), \(10~\text{V}\) and \(40~\text{V}\), respectively. The amplitude of the current flowing through the \(LCR\) series circuit is \(10\sqrt{2}~\text{A}\). The impedance of the circuit will be:

      
1. \(4~\Omega\)
2. \(5~\Omega\)
3. \(4\sqrt{2}~\Omega\)
4. \(\frac{5}{\sqrt{2}}~\Omega\)

The equivalent capacitance of the combination shown in the figure is: 

Consider the following Statements (A) and (B) and identify the correct answer. 

The number of photons per second on an average emitted by a source of monochromatic light of wavelength \(600~\text{nm}\), when it delivers the power of \(3.3\times 10^{-3}\) watt will be: \((h = 6.6\times10^{-34}~\text{J-s})\)
1. \(10^{16}\)
2. \(10^{15}\)
3. \(10^{18}\)
4. \(10^{17}\)$$

A parallel plate capacitor has a uniform electric field \(\vec{E}\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A\) the energy stored in the capacitor is: 
\(\left ( \varepsilon_{0} = \text{permittivity of free space} \right )\)
1. \(\frac{1}{2}\varepsilon_0 E^2 Ad\)
2. \(\frac{E^2 Ad}{\varepsilon_0}\)
3. \(\frac{1}{2}\varepsilon_0 E^2 \)
4. \(\varepsilon_0 EAd\)

A capacitor of capacitance \(C\) is connected across an AC source of voltage \(V\), given by;
\(V=V_0 \sin \omega t\)$\mathrm{}$
The displacement current between the plates of the capacitor would then be given by:
1. \( I_d=\frac{V_0}{\omega C} \sin \omega t \)
2. \( I_d=V_0 \omega C \sin \omega t \)
3. \( I_d=V_0 \omega C \cos \omega t \)
4. \( I_d=\frac{V_0}{\omega C} \cos \omega t\)

Two charged spherical conductors of radii \(R_1\) and \(R_2\) are connected by a wire. The ratio of surface charge densities of spheres \(\left ( \frac{\sigma _{1}}{\sigma _{2}}\right )\) is:
1. \(\sqrt{\frac{R_1}{R_2}}\)
2. \(\frac{R^2_1}{R^2_2}\)
3. \(\frac{R_1}{R_2}\)
4. \(\frac{R_2}{R_1}\)

An electromagnetic wave of wavelength \(\lambda\) is incident on a photosensitive surface of negligible work function. If '\(m\)' is the mass of photoelectron emitted from the surface and \(\lambda_d\) is the de-Broglie wavelength, then:
1. \( \lambda=\left(\frac{2 {mc}}{{h}}\right) \lambda_{{d}}^2 \)
2. \( \lambda=\left(\frac{2 {h}}{{mc}}\right) \lambda_{{d}}^2 \)
3. \( \lambda=\left(\frac{2 {m}}{{hc}}\right) \lambda_{{d}}^2\)
4. \( \lambda_{{d}}=\left(\frac{2 {mc}}{{h}}\right) \lambda^2 \)

A spring is stretched by \(5~\text{cm}\) by a force \(10~\text{N}\). The time period of the oscillations when a mass of \(2~\text{kg}\) is suspended by it is:
1. \(3.14~\text{s}\)
2. \(0.628~\text{s}\)
3. \(0.0628~\text{s}\)
4. \(6.28~\text{s}\)