Three uncharged capacitors of capacities \(C_1, C_2~\text{and}~C_3\) are connected to one another as shown in the figure.
If points A, B, and D, are at potential \(V_1, V_2 ~\text{and}~V_3\) then the potential at O will be:
1. | \(\frac{V_1C_1+V_2C_2+V_3C_3}{C_1+C_2+C_3}\) | 2. | \(\frac{V_1+V_2+V_3}{C_1+C_2+C_3}\) |
3. | \(\frac{V_1(V_2+V_3)}{C_1(C_2+C_3)}\) | 4. | \(\frac{V_1V_2V_3}{C_1C_2C_3}\) |
1. | \(0.6\) m/s | 2. | \(6\) m/s |
3. | \(2\) m/s | 4. | \(4\) m/s |
Figure shows a ball having a charge \(q\) fixed at a point . Two identical balls having charges \(+q\) and \(–q\) and mass \(‘m’\) each are attached to the ends of a light rod of length \(2 a\)
1. | \(\frac{\sqrt{2}q}{3 \pi \varepsilon_0 {ma}^3} \) | 2. | \(\frac{q}{\sqrt{3 \pi \varepsilon_0 {ma}^3 }}\) |
3. | \(\frac{q}{\sqrt{6 \pi \varepsilon_0 {ma}^3 }} \) | 4. | \(\frac{\sqrt{2} q}{4 \pi \varepsilon_0 m a^3} \) |
1. | \(2\) kV | 2. | \(4\) kV |
3. | \(6\) kV | 4. | \(9\) kV |
The electrostatic force between the metal plates of an isolated parallel plate capacitor \(C\) having a charge \(Q\) and area \(A\) is:
1. | independent of the distance between the plates. |
2. | linearly proportional to the distance between the plates. |
3. | proportional to the square root of the distance between the plates. |
4. | inversely proportional to the distance between the plates. |
Maximum charge stored on a metal sphere of radius \(15\) cm may be \(7.5~\mu\text{C}\). The potential energy of the sphere in this case is:
1. \(9.67\) J
2. \(0.25\) J
3. \(3.25\) J
4. \(1.69\) J
Four electric charges \(+ q,\) \(+ q,\) \(- q\) and \(- q\) are placed at the corners of a square of side \(2L\) (see figure). The electric potential at point \(A\), mid-way between the two charges \(+ q\) and \(+ q\) is:
1. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 + \frac{1}{\sqrt{5}}\right)\)
2. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 - \frac{1}{\sqrt{5}}\right)\)
3. zero
4. \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L} \left(1 + \sqrt{5}\right)\)
1. | \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_{\mathrm{A}} \neq \mathrm{V}_{\mathrm{B}}\) |
2. | \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B \neq \mathrm{V}_{\mathrm{A}}\) |
3. | \(\mathrm{V}_{\mathrm{C}} \neq \mathrm{V}_B \neq \mathrm{V}_A\) |
4. | \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B=\mathrm{V}_A\) |
The electric potential at a point in free space due to a charge \(Q\) coulomb is \(Q\times10^{11}~\text{V}\). The electric field at that point is:
1. \(4\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
2. \(12\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
3. \(4\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
4. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
Two condensers, one of capacity \(C\) and the other of capacity \(\frac{C}2\) are connected to a \(V\) volt battery, as shown in the figure.
The energy stored in the capacitors when both condensers are fully charged will be:
1. \(2CV^2\)
2. \({1 \over4}CV^2\)
3. \({3 \over4}CV^2\)
4. \({1 \over2}CV^2\)