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 \(2V.\) 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. \(\frac{9 C V^{2}}{2}\)

Condenser A has a capacity of 15 μF when it is filled with a medium of dielectric constant 15. Another condenser B has a capacity of 1 μF with air between the plates. Both are charged separately by a battery of 100 V. After charging, both are connected in parallel without the battery and the dielectric medium being removed. The common potential now is 

(1) 400 V

(2) 800 V

(3) 1200 V

(4) 1600 V

Four metallic plates each with a surface area of one side A are placed at a distance d from each other. The plates are connected as shown in the circuit diagram. Then the capacitance of the system between a and b is

(1) $\frac{3{\epsilon }_{0}A}{d}$

(2) $\frac{2{\epsilon }_{0}A}{d}$

(3) $\frac{2{\epsilon }_{0}A}{3d}$

(4) $\frac{3{\epsilon }_{0}A}{2d}$

In the given circuit if point C is connected to the earth and a potential of +2000 V is given to the point A, the potential at B is 

(1) 1500 V

(2) 1000 V

(3) 500 V

(4) 400 V

A finite ladder is constructed by connecting several sections of 2 μF, 4 μF capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between 

(1) 4 μF

(2) 2 μF

(3) 18 μF

(4) 6 μF

In an isolated parallel plate capacitor of capacitance C, the four surface have charges Q₁, Q₂, Q₃ and Q₄ as shown. The potential difference between the plates is 

(1) $\frac{Q_1+Q_2+Q_3+Q_4}{2C}$

(2) $\frac{Q_2+Q_3}{2C}$

(3) $\frac{Q_2-Q_3}{2C}$

(4) $\frac{Q_1+Q_4}{2C}$

For the circuit shown, which of the following statements is true 

(1) With S₁ closed, V₁ = 15 V, V₂ = 20 V

(2) With S₃ closed V₁ = V₂ = 25 V

(3) With S₁ and S₂ closed V₁ = V₂ = 0

(4) With S₁ and S₃ closed, V₁ = 30 V, V₂ = 20 V

Consider the situation shown in the figure. The capacitor \(A\) has a charge \(q\) on it whereas \(B\) is uncharged. The charge appearing on the capacitor \(B\) a long time after the switch is closed is: 

1. zero
2. \(\frac{q}{2}\)
3. \(q\)
4. \(2q\)

A capacitor of capacitance C₁ = 1 μF can withstand maximum voltage V₁ = 6kV (kilo-volt) and another capacitor of capacitance C₂ = 3 μF can withstand maximum voltage V₂ = 4 kV. When the two capacitors are connected in series, the combined system can withstand a maximum voltage of

(1) 4 kV

(2) 6 kV

(3) 8 kV

(4) 10 kV

The plates of a parallel plate condenser are pulled apart with a velocity v. If at any instant their mutual distance of separation is d, then the magnitude of the time rate of change of capacity depends on d as follows 

(1) 1/d

(2) 1/d²

(3) d²

(4) d