Q. No.Three identical capacitors are connected as follows:
Which of the following shows the order of increasing capacitance (smallest first)?
1.
\(\mathrm{(3), (2), (1)}\)
2.
\(\mathrm{(1), (2), (3)}\)
3.
\(\mathrm{(2), (1), (3)}\)
4.
\(\mathrm{(2), (3), (1)}\)
Which of the following shows the order of increasing capacitance (smallest first)?
In the given figure if \(V = 4~\text{volt}\) each plate of the capacitor has a surface area of\(10^{-2}~\text{m}^2\) and the plates are \(0.1\times10^{-3}~\text{m}\)apart, then the number of excess electrons on the negative plate is:
1. \(5.15\times 10^{9}\)
2. \(2.21\times 10^{10}\)
3. \(3.33\times 10^{9}\)
4. \(2.21\times 10^{9}\)
An electric dipole of moment \(p\) is placed in an electric field of intensity \(E\). The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ},\) the torque and the potential energy of the dipole will respectively be:
| 1. | \(p E \sin \theta,-p E \cos \theta\) | 2. | \(p E \sin \theta,-2 p E \cos \theta\) |
| 3. | \(p E \sin \theta, 2 p E \cos \theta\) | 4. | \(p E \cos \theta,-p E \sin \theta\) |
Two identical capacitors \(C_{1}\) and \(C_{2}\) of equal capacitance are connected as shown in the circuit. Terminals \(a\) and \(b\) of the key \(k\) are connected to charge capacitor \(C_{1}\) using a battery of emf \(V\) volt. Now disconnecting \(a\) and \(b\) terminals, terminals \(b\) and \(c\) are connected. Due to this, what will be the percentage loss of energy?
| 1. | \(75\%\) | 2. | \(0\%\) |
| 3. | \(50\%\) | 4. | \(25\%\) |
1. \(\sigma_{1}=\dfrac{5}{6}\sigma ,~\sigma_{2}=\dfrac{5}{6}\sigma\)
2. \(\sigma_{1}=\dfrac{5}{2}\sigma ,~\sigma_{2}=\dfrac{5}{6}\sigma\)
3. \(\sigma_{1}=\dfrac{5}{2}\sigma ,~\sigma_{2}=\dfrac{5}{3}\sigma\)
4. \(\sigma_{1}=\dfrac{5}{3}\sigma ,~\sigma_{2}=\dfrac{5}{6}\sigma\)
The graph of electric potential \((V)\) versus distance \((r)\) is shown in the diagram. The value of the electric field at a distance \(A\) will be:
| 1. | \(5\) V/m | 2. | \(-10\) V/m |
| 3. | \(-5\) V/m | 4. | \(10\) V/m |
Two capacitors of capacity \(2~\mu\text{F}\) and \(3~\mu\text{F}\) are charged to the same potential difference of \(6~\text V.\) Now they are connected with opposite polarity as shown. After closing switches \(S_1~\text{and}~S_2\), their final potential difference becomes:
| 1. | \(\text{zero} \) | 2. | \(\frac{4}{3}~\text{V} \) |
| 3. | \(3~\text{V} \) | 4. | \(\frac{6}{5}~\text{V} \) |
Which of the following statements is correct regarding the electrostatics of conductors?
| 1. | The interior of the conductor with no cavity can have no excess charge in the static situation. |
| 2. | The electrostatic potential is constant throughout the volume of the conductor. |
| 3. | The electrostatic potential has the same value inside as that on its surface. |
| 4. | All of the above statements are correct. |
Some equipotential surfaces are shown in the figure. The electric field at points \(A\), \(B\) and \(C\) are respectively:
| 1. | \(1~\text{V/cm}, \frac{1}{2} ~\text{V/cm}, 2~\text{V/cm} \text { (all along +ve X-axis) }\) |
| 2. | \(1~\text{V/cm}, \frac{1}{2} ~\text{V/cm}, 2 ~\text{V/cm} \text { (all along -ve X-axis) }\) |
| 3. | \(\frac{1}{2} ~\text{V/cm}, 1~\text{V/cm}, 2 ~\text{V/cm} \text { (all along +ve X-axis) }\) |
| 4. | \(\frac{1}{2}~\text{V/cm}, 1~\text{V/cm}, 2 ~\text{V/cm} \text { (all along -ve X-axis) }\) |
The variation of potential with distance \(x\) from a fixed point is shown in the figure. The electric field at \(x=13~\text m\) is:
| 1. | \(7.5~\text{V/m}\) | 2. | \(-7.5~\text{V/m}\) |
| 3. | \(5~\text{V/m}\) | 4. | \(-5~\text{V/m}\) |
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