If the dielectric constant and dielectric strength be denoted by \(k\) and \(x\) respectively, then a material suitable for use as a dielectric in a capacitor must have:
1. high \(k\) and high \(x\).
2. high \(k\) and low \(x\).
3. low \(k\) and low \(x\).
4. low \(k\) and high \(x\).
Three capacitors of capacitances \(3~\mu\text{F}\), \(9~\mu\text{F}\) and \(18~\mu\text{F}\) are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases \(\frac{C_s}{C_p}\) will be:
1. \(1:15\)
2. \(15:1\)
3. \(1:1\)
4. \(1:3\)
Four capacitors each of capacity \(3~\mu\text{F}\) are connected as shown in the adjoining figure. The ratio of equivalent capacitance between \(A\) and \(B\) and between \(A\) and \(C\) will be:
1. \(4:3\)
2. \(3:4\)
3. \(2:3\)
4. \(3:2\)
A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is \(A\) metre2 and the separation is \(t\) metre. The dielectric constants are \(k_1\) and \(k_2\) respectively. Its capacitance in farad will be:
1. \(\frac{\varepsilon_{0} A}{t} \left( k_{1} + k_{2}\right)\)
2. \(\frac{\varepsilon_{0} A}{t} \frac{\left( k_{1} + k_{2}\right)}{2}\)
3. \(\frac{2\varepsilon_{0} A}{t} \left( k_{1} + k_{2}\right)\)
4. \(\frac{\varepsilon_{0} A}{t} \frac{\left( k_{1} - k_{2}\right)}{2}\)
In the connections shown in the adjoining figure, the equivalent capacity between \(A\) and \(B\) will be:
1. \(10.8~\mu\text{F}\)
2. \(69~\mu\text{F}\)
3. \(15~\mu\text{F}\)
4. \(10~\mu\text{F}\)
The diagrams below show regions of equipotentials.
1. | the maximum work is required to move \(q\) in figure(iii). |
2. | in all four cases, the work done is the same. |
3. | the minimum work is required to move \(q\) in the figure(i). |
4. | the maximum work is required to move \(q\) in figure(ii). |
A capacitor of \(2~\mu\text{F}\) is charged as shown in the figure. When the switch \(S\) is turned to position \(2\), the percentage of its stored energy dissipated is:
1. | \(20\%\) | 2. | \(75\%\) |
3. | \(80\%\) | 4. | \(0\%\) |
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. \(1\times 10^{-2}~\text{C}\)