1. | The potential difference between the plates decreases \(K\) times |
2. | The energy stored in the capacitor decreases \(K\) times |
3. | The change in energy stored is \({1 \over 2} CV^{2}(\frac{1}{K}-1)\) |
4. | The charge on the capacitor is not conserved |
\(A,B\) and \(C\) are three points in a uniform electric field. The electric potential is:
1. | maximum at \(A\) |
2. | maximum at \(B\) |
3. | maximum at \(C\) |
4. | same at all the three points \(A,B\) and \(C\) |
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. \(1\times 10^{-2}~\text{C}\)
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. | \(\dfrac{E^2Ad}{\varepsilon_0}\) |
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. \(\frac{16C_1}{n_1n_2}\)
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 |
The equivalent capacitance between \(A\) and \(B\) is:
1. | \(2~\mu\text{F}\) | 2. | \(3~\mu\text{F}\) |
3. | \(5~\mu\text{F}\) | 4. | \(0.5~\mu\text{F}\) |
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?
1. | \(\left|\vec{E}_1\right|=\left|\vec{E}_2\right|, V_1=V_2\) |
2. | \(\vec{E}_1 \neq \vec{E}_2, V_1 \neq V_2\) |
3. | \(\vec{E}_1 \neq \vec{E}_2, V_1=V_2\) |
4. | \(\left|\vec{E}_1\right|=\left|\vec{E}_2\right|, V_1 \neq V_2\) |
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?
1. | \(\frac{Z e^2}{2 \pi \varepsilon_0 m v^2} \) | 2. | \(\frac{Z_e}{4 \pi \varepsilon_0 m v^2} \) |
3. | \(\frac{Z e^2}{8 \pi \varepsilon_0 m v^2} \) | 4. | \(\frac{Z_e}{8 \pi \varepsilon_0 m v^2}\) |