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. | \(15\) | 2. | \(7.5\) |
3. | \(0.3\) | 4. | \(150\) |
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. | \(25\%\) |
(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 |
1. | \(1.5\times 10^{-6}~\text{J}\) | 2. | \(4.5\times 10^{-6}~\text{J}\) |
3. | \(3.25\times 10^{-6}~\text{J}\) | 4. | \(2.25\times 10^{-6}~\text{J}\) |