A parallel plate capacitor has capacitance \(C\). If it is equally filled with parallel layers of materials of dielectric constants \(K_1\) and \(K_2\), its capacity becomes \(C_1\). The ratio of \(C_1\) to \(C\) is:

1.	\(K_1 + K_2\)	2.	\(\frac{K_{1} K_{2}}{K_{1}-K_{2}}\)
3.	\(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\)	4.	\(\frac{2 K_{1} K_{2}}{K_{1}+K_{2}}\)

Consider two points \(1\) and \(2\) in a region outside a charged sphere. Two points are not very far away from the sphere. If \(E\) and \(V\) represent the electric field vector and the electric potential, which of the following is not possible?

An elementary particle of mass \(m\) and charge \(+e\) is projected with velocity \(v\) at a much more massive particle of charge \(Ze\), where \(Z>0\). What is the closest possible approach of the incident particle?

A parallel plate capacitor of capacitance \(C\) is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance \(2C\) is connected to another battery and is charged to potential difference \(2\)V. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is?
1. zero
2. \(\frac{25 C V^{2}}{6}\)
3. \(\frac{3 C V^{2}}{2}\)
4. \(\frac{9 C V^{2}}{2}\)

The equivalent capacitance between \(A\) and \(B\) is:

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 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. \(\frac{1}{2}\varepsilon_0 E^2\)
2. \(\varepsilon_0 EAd\)
3. \(\frac{1}{2}\varepsilon_0 E^2Ad\)
4. \(\frac{E^2Ad}{\varepsilon_0}\)

Two metallic spheres of radii \(1\) cm and \(3\) cm are given charges of \(-1\times 10^{-2}~\text{C}\) and \(5\times 10^{-2}~\text{C},\) respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:
1. \(2\times 10^{-2}~\text{C}\)
2. \(3\times 10^{-2}~\text{C}\)
3. \(4\times 10^{-2}~\text{C}\)
4. \(1\times 10^{-2}~\text{C}\)

\(\mathrm{A}\), \(\mathrm{B}\) and \(\mathrm{C}\) are three points in a uniform electric field. The electric potential is: