Q. No.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. | \(\varepsilon_0 EAd\) |
(Assuming the charge on plates remains constant)
| 1. | \(6 E,6 C\) | 2. | \( E,C\) |
| 3. | \(\frac{E}{6},6C\) | 4. | \(E,6C\) |
A series combination of \(n_1\) capacitors, each of value \(C_1\), is charged by a source of potential difference \(4\) V. When another parallel combination of \(n_2\) capacitors, each of value \(C_2\), is charged by a source of potential difference \(V\), it has the same (total) energy stored in it as the first combination has. The value of \(C_2\) in terms of \(C_1\) is:
1. \(\frac{2C_1}{n_1n_2}\)
2. \(16\frac{n_2}{n_1}C_1\)
3. \(2\frac{n_2}{n_1}C_1\)
4. \(\frac{16C_1}{n_1n_2}\)
| (A) | The charge stored in it increases. |
| (B) | The energy stored in it decreases. |
| (C) | Its capacitance increases. |
| (D) | The ratio of charge to its potential remains the same. |
| (E) | The product of charge and voltage increases. |
| 1. | (A), (C) and (E) only |
| 2. | (B), (D) and (E) only |
| 3. | (A), (B) and (C) only |
| 4. | (A), (B) and (E) only |
A parallel plate condenser has a uniform electric field \(E\)(V/m) in the space between the plates. If the distance between the plates is \(d\)(m) and area of each plate is \(A(\text{m}^2)\), the energy (joule) stored in the condenser is:
| 1. | \(\dfrac{1}{2}\varepsilon_0 E^2\) | 2. | \(\varepsilon_0 EAd\) |
| 3. | \(\dfrac{1}{2}\varepsilon_0 E^2Ad\) | 4. | \(\dfrac{E^2Ad}{\varepsilon_0}\) |
| 1. | \(10^{7}\) joule and \(300\) paise |
| 2. | \(5\times 10^{6}\) joule and \(300\) paise |
| 3. | \(5\times 10^{6}\) joule and \(150\) paise |
| 4. | \(10^7\) joule and \(150\) paise |
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
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. \({1 \over2}CV^2\)
Five equal capacitors connected in series have a resultant capacitance of \(4~\mu\text{F}\). The total energy stored in these when these are connected in parallel and charged to \(400\) V is:
1. \(1~\text{J}\)
2. \(8~\text{J}\)
3. \(16~\text{J}\)
4. \(4~\text{J}\)
Two condensers of capacity \(0.3~\mu\text{F}\) and \(0.6~\mu\text{F}\) are connected in series. The combination is connected across a potential of \(6\) V. The ratio of energies stored by the condensers will be:
1. \(\frac{1}{2}\)
2. \(2\)
3. \(\frac{1}{4}\)
4. \(4\)
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