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

In a hollow spherical shell potential (V) changes with respect to distance (r) from centre 

(1)

(2)

(3)

(4)

What physical quantities may X and Y represent ? (Y represents the first mentioned quantity) 

(1) Pressure v/s temperature of a given gas (constant volume)

(2) Kinetic energy v/s velocity of a particle

(3) Capacitance v/s charge to give a constant potential

(4) Potential v/s capacitance to give a constant charge

Between the plates of a parallel plate capacitor a dielectric plate is introduced just to fill the space between the plates. The capacitor is charged and later disconnected from the battery. The dielectric plate is slowly drawn out of the capacitor parallel to the plates. The plot of the potential difference across the plates and the length of the dielectric plate drawn out is

(1)

(2)

(3)

(4)

Figure (a) shows two capacitors connected in series and joined to a battery. The graph in figure (b) shows the variation in potential difference as one moves from left to right  on the branch containing the capacitors, if 

(1) C₁ > C₂

(2) C₁ = C₂

(3) C₁ < C₂

(4) The information is not sufficient to decide the relation between C₁ and $C_2$

Equipotential surfaces are shown in figure. Then the electric field strength will be

(1) 100 Vm^–1 along X-axis

(2) 100 Vm^–1 along Y-axis

(3) 200 Vm^–1 at an angle 120^o with X-axis

(4) 50 Vm^–1 at an angle 120^o with X-axis

A condenser of 2μF capacitance is charged steadily from 0 to 5 Coulomb. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to the charge on the condenser?

(1)

(2)

(3)

(4)