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

A fully charged capacitor has a capacitance ‘C’. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity ‘s’ and mass ‘m’. If the temperature of the block is raised by ‘ΔT’, the potential difference ‘V’ across the capacitance is 

(1) $\frac{ms\Delta T}{C}$

(2) $\sqrt{\frac{2ms\Delta T}{C}}$

(3) $\sqrt{\frac{2mC\Delta T}{s}}$

(4) $\frac{mC\Delta T}{s}$

A network of four capacitors of capacity equal to $C_1=C,C_2=2C,C_3=3C$ and C₄ = 4 C are connected in a battery as shown in the figure. The ratio of the charges on C₂ and C₄ is 

(1) $\frac{22}{3}$

(2) $\frac{3}{22}$

(3) $\frac{7}{4}$

(4) $\frac{4}{7}$

The variation of potential with distance R from a fixed point is as shown below. The electric field at R = 5 m is 

(1) 2.5 volt/m

(2) –2.5 volt/m

(3) 2/5 volt/m

(4) –2/5 volt/m

The figure gives the electric potential V as a function of distance through five regions on x-axis. Which of the following is true for the electric field E in these regions 

(1) $E_1>E_2>E_3>E_4>E_5$

(2) $E_1=E_3=E_5$ and $E_2<E_4$

(3) $E_2=E_4=E_5$ and $E_1<E_3$

(4) $E_1<E_2<E_3<E_4<E_5$