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. \({1 \over2}CV^2\)

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:

Surface charge density on the positive plate of a charged parallel plate capacitor is \(\sigma.\) Energy density in the electric field of the capacitor is:
1. \(\frac{\sigma^2}{\varepsilon_0}\)
2. \(\frac{\sigma^2}{2\varepsilon_0}\)
3. \(\frac{\sigma}{\varepsilon_0}\)
4. \(2\sigma^2 \varepsilon_0\)

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. \(4~\text{J}\)

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. \(\frac{16C_1}{n_1n_2}\)

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. \(4\)

In the circuit shown in the figure, the energy stored in \(6~\mu\text{F}\) capacitor will be: