Q. No.Twenty seven drops of same size are charged at \(220~\text{V}\) each. They combine to form a bigger drop. Calculate the potential of the bigger drop:
1.
\(1520~\text{V}\)
2.
\(1980~\text{V}\)
3.
\(660~\text{V}\)
4.
\(1320~\text{V}\)
| 1. | \(\sqrt{\dfrac{R_1}{R_2}}\) | 2. | \(\dfrac{R^2_1}{R^2_2}\) |
| 3. | \(\dfrac{R_1}{R_2}\) | 4. | \(\dfrac{R_2}{R_1}\) |
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. \(\varepsilon_0 EAd\)
The equivalent capacitance of the combination shown in the figure is:
| 1. | \(\dfrac{C}{2}\) | 2. | \(\dfrac{3C}{2}\) |
| 3. | \(3C\) | 4. | \(2C\) |
Three capacitors each of capacity \(4\) µF are to be connected in such a way that the effective capacitance is \(6\) µF. This can be done by:
| 1. | connecting all of them in a series. |
| 2. | connecting them in parallel. |
| 3. | connecting two in series and one in parallel. |
| 4. | connecting two in parallel and one in series. |
Energy per unit volume for a capacitor having area \(A\) and separation \(d\) kept at a potential difference \(V\) is given by:
| 1. | \(\dfrac{1}{2}\varepsilon_0\dfrac{V^2}{d^2}\) | 2. | \(\dfrac{1}{2}\dfrac{V^2}{\varepsilon_0d^2}\) |
| 3. | \(\dfrac{1}{2}CV^2\) | 4. | \(\dfrac{Q^2}{2C}\) |
If identical charges \((-q)\) are placed at each corner of a cube of side \(b\) then the electrical potential energy of charge \((+q)\) which is placed at centre of the cube will be:
| 1. | \(\dfrac{- 4 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}\) | 2. | \(\dfrac{- 8 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}\) |
| 3. | \(\dfrac{- 4 q^{2}}{\sqrt{3} \pi\varepsilon_{0} b}\) | 4. | \(\dfrac{8 \sqrt{2} q^{2}}{4 \pi\varepsilon_{0} b}\) |
A capacitor of capacity \(C_1\) is charged up to \(V\) volt and then connected to an uncharged capacitor \(C_2\). Then final P.D. across each will be:
1. \(\frac{C_{2} V}{C_{1} + C_{2}}\)
2. \(\frac{C_{1} V}{C_{1} + C_{2}}\)
3. \(\left(1 + \frac{C_{2}}{C_{1}}\right)\)
4. \(\left(1 - \frac{C_{2}}{C_{1}} \right) V\)
Some charge is being given to a conductor. Then it's potential:
| 1. | is maximum at the surface. |
| 2. | is maximum at the centre. |
| 3. | remains the same throughout the conductor. |
| 4. | is maximum somewhere between the surface and the centre. |
(Assuming the charge on plates remains constant)
| 1. | \(6 E,6 C\) | 2. | \( E,C\) |
| 3. | \(\frac{E}{6},6C\) | 4. | \(E,6C\) |
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