The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section, and same material is \(0.25~\Omega\). What will be the effective resistance if they are connected in series?
1. \(1~\Omega\)
2. \(4~\Omega\)
3. \(0.25~\Omega\)
4. \(0.5~\Omega\)
1. \(1~\Omega\)
2. \(4~\Omega\)
3. \(0.25~\Omega\)
4. \(0.5~\Omega\)
| 1. | \(\beta^{+}, ~\alpha, ~\beta^{-}\) | 2. | \(\beta^{-}, ~\alpha, ~\beta^{+}\) |
| 3. | \(\alpha, ~\beta^{-},~\beta^{+}\) | 4. | \(\alpha, ~\beta^{+},~\beta^{-}\) |
A dipole is placed in an electric field as shown. In which direction will it move?
| 1. | towards the left as its potential energy will decrease. |
| 2. | towards the right as its potential energy will increase. |
| 3. | towards the left as its potential energy will increase. |
| 4. | towards the right as its potential energy will decrease. |
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. \(\dfrac{5}{\sqrt{2}}~\Omega\)
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. | \( I_d=\dfrac{V_0}{\omega C} \cos \omega t\) |
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