1000 small water drops, each of capacitance C, join together to form one large spherical drop. The capacitance of the bigger sphere is:

1. C

2. 10C

3. 100C

4. 1000C

Two similar conducting balls having charges +q and -q are placed at a separation d from each other in the air. The radius of each ball is r and the separation between their centres is d(d>>r). Calculate the capacitance of the two-ball system.

1. $4{\mathrm{\pi \epsilon }}_0\mathrm{r}$

2. $2{\mathrm{\pi \epsilon }}_0\mathrm{r}$

3. $4{\mathrm{\pi log}}_{\mathrm{e}}\frac{{\mathrm{\epsilon }}_0\mathrm{r}}{\mathrm{d}}$

4. $4{\mathrm{\pi log}}_{\mathrm{e}}\frac{\mathrm{r}}{\mathrm{d}}$

Two parallel plate capacitors have their plate areas 100 cm² and 500 cm² respectively. If they have the same charge and potential and the distance between the plates of the first capacitor is 0.5 mm, then the distance between the plates of the second capacitor is:

1. 0.10 cm

2. 0.15 cm

3. 0.20 cm

4. 0.25 cm

A dielectric slab of dielectric constant K is placed between the plates of a parallel plate capacitor carrying charge q. The induced charge q' on the surface of the slab is given by:

1. $\mathrm{q}\text{'}=\mathrm{q}-\frac{\mathrm{q}}{\mathrm{K}}$

2. $\mathrm{q}\text{'}=-\mathrm{q}+\frac{\mathrm{q}}{\mathrm{K}}$

3. $\mathrm{q}\text{'}=\mathrm{q}\left[\frac{1}{\mathrm{K}}+1\right]$

4. $\mathrm{q}\text{'}=-\mathrm{q}\left(1+\frac{1}{\mathrm{K}}\right)$

Two charge capacitors have their outer plates fixed and inner plates connected by a spring of force constant 'k'. The charge on each capacitor is q. Find the extension in the spring at equilibrium

1. $\frac{{\mathrm{q}}^2}{2{\mathrm{A\epsilon }}_0\mathrm{k}}$

2. $\frac{{\mathrm{q}}^2}{4{\mathrm{A\epsilon }}_0\mathrm{k}}$

3. $\frac{{\mathrm{q}}^2}{{\mathrm{A\epsilon }}_0\mathrm{k}}$

4. Zero

The following arrangement consists of five identical metal plates parallel to each other. The area of such plate is A and separation between the successive plates is d. The capacitance between P and Q is:

1. $\frac{5{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

2. $\frac{7}{3}{\mathrm{\epsilon }}_0\frac{\mathrm{A}}{\mathrm{d}}$

3. $\frac{4}{3}\frac{{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

4. $\frac{5}{3}\frac{{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

A capacitor is half-filled with a dielectric (K=2) as shown in figure A. If the same capacitor is to be filled with the same dielectric as shown in figure B, what would be the thickness of the dielectric so that the capacitor still has the same capacity?

1. 2d/3

2. 3d/2

3. 3d/4

4. 4d/3

Capacitors ${\mathrm{C}}_1\left(10\mathrm{\mu F}\right)$ and ${\mathrm{C}}_2\left(20\mathrm{\mu F}\right)$ are connected in series across a 3 kV supply as shown. What is the charge on the capacitor C₁?

1. $45000 \mathrm{\mu C}$

2. $20000 \mathrm{\mu C}$

3. $15000 \mathrm{\mu C}$

4. $10000 \mathrm{\mu C}$

The charge on the 6 $\mathrm{\mu F}$ capacitors in the circuit shown is:

1. $540 \mathrm{\mu C}$

2. $270 \mathrm{\mu C}$

3. $180 \mathrm{\mu C}$

4. $90 \mathrm{\mu C}$

In the circuit below ${\mathrm{C}}_1=20\mathrm{\mu F}, {\mathrm{C}}_2=40\mathrm{\mu F}$ and ${\mathrm{C}}_3=50\mathrm{\mu F}$. If no capacitor can sustain more than 50 V, then the maximum potential difference between X and Y is:

1. 95 V

2. 75 V

3. 150 V

4. 65 V