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. \(\dfrac{5}{\sqrt{2}}~\Omega\)
1. \(4~\Omega\)
2. \(5~\Omega\)
3. \(4\sqrt{2}~\Omega\)
4. \(\dfrac{5}{\sqrt{2}}~\Omega\)
The equivalent capacitance of the combination shown in the figure is:
1. \(\dfrac{C}{2}\)
2. \(\dfrac{3C}{2}\)
3. \(3C\)
4. \(2C\)
| Statement A: | A Zener diode is connected in reverse bias when used as a voltage regulator. |
| Statement B: | The potential barrier of \(\mathrm{p\text-n}\) junction lies between \(0.2\) V to \(0.3\) V. |
| 1. | Statement A is correct and Statement B is incorrect. |
| 2. | Statement A is incorrect and Statement B is correct. |
| 3. | Statement A and Statement B both are correct. |
| 4. | Statement A and Statement B both are incorrect. |
| 1. | \(\hat{j}+\hat{k},~-\hat{j}-\hat{k}\) | 2. | \(-\hat{j}+\hat{k},~-\hat{j}+\hat{k}\) |
| 3. | \(\hat{j}+\hat{k},~\hat{j}+\hat{k}\) | 4. | \(-\hat{j}+\hat{k},~-\hat{j}-\hat{k}\) |
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. | \(\dfrac{1}{2}\varepsilon_0 E^2 Ad\) | 2. | \(\dfrac{E^2 Ad}{\varepsilon_0}\) |
| 3. | \(\dfrac{1}{2}\varepsilon_0 E^2 \) | 4. | \(\varepsilon_0 EAd\) |
\(V=V_0 \sin \omega t\)
The displacement current between the plates of the capacitor would then be given by:
| 1. | \( I_d=\dfrac{V_0}{\omega C} \sin \omega t \) | 2. | \( I_d=V_0 \omega C \sin \omega t \) |
| 3. | \( I_d=V_0 \omega C \cos \omega t \) | 4. | \( I_d=\dfrac{V_0}{\omega C} \cos \omega t\) |
| 1. | \(\sqrt{\dfrac{R_1}{R_2}}\) | 2. | \(\dfrac{R^2_1}{R^2_2}\) |
| 3. | \(\dfrac{R_1}{R_2}\) | 4. | \(\dfrac{R_2}{R_1}\) |
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. | \( \lambda=\left(\dfrac{2 {mc}}{{h}}\right) \lambda_{{d}}^2 \) | 2. | \( \lambda=\left(\dfrac{2 {h}}{{mc}}\right) \lambda_{{d}}^2 \) |
| 3. | \( \lambda=\left(\dfrac{2 {m}}{{hc}}\right) \lambda_{{d}}^2\) | 4. | \( \lambda_{{d}}=\left(\dfrac{2 {mc}}{{h}}\right) \lambda^2 \) |
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. \(6.28~\text{s}\)
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