Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field  in the gap to the original electric field  is __.

A co-axial cylindrical capacitor shown in figure (i) has dielectric with relative permittivity. When one-fourth portion of the dielectric is replaced with another dielectric of relative permittivity, as shown in Figure (ii), the capacitance is doubled. The value of  is ___

The capacitance of an air-filled parallel-plate capacitor is 60pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _______ (up to 2 decimal places).        

A parallel plate capacitor filled with two dielectric is shown in the figure below, If the electric field in the region A is 4 kV/cm, the electric field in the region B, in kV/cm, is

A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strength of air and glass are 30kV/cm and 300kV/cm, respectively. The maximum voltage (in kilovolts) which can be applied across the capacitor without any breakdown is _____________.

is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity, the expression for the modified capacitance is

A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is placed symmetrical with respect to the plates.

If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio  is

Three capacitors , , and , whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum safe voltage in volts that can be applied across the combination and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively         

In the following figure,  and  are ideal capacitors.  has been charged to 12V before the ideal switch S is closed at t = 0. The current i(t) for all t is

A capacitor is made with a polymeric dielectric having an of 2.26 and a dielectric breakdown strength of 50kV/cm. The permittivity of free space is 8.85pF/m. If the rectangular plates of the capacitor have a width of 20cm and a length of 40cm, then the maximum electric charge in the capacitor is

A capacitor consists of two metal plates each  and spaced 6 mm apart. The space between the metal plates is filled with a glass plate of 4 mm thickness and a layer of paper of 2 mm thickness. The relative permittivity of the glass and paper are 8 and 2 respectively. Neglecting the fringing effect, the capacitance will be

(Given that )

A parallel plate capacitor is shown in figure. It is made of two square metal plates of 400 mm side. The 14 mm space between the plates is filled with two layers of dielectrics of , 6 mm thick and , 8 mm thick.  Neglecting fringing of fields at the edges the capacitance is

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ( and ) as shown in Figure. The two different dielectric materials are separated by a conducting foil F. The voltage of the conducting foil is

A charge +Q uniformly distributed throughout the volume of a dielectric sphere of radius R and dielectric constant based on Gauss law, determine the expressions for the electric field E as a function of distance r from the centre of the sphere, within the ranges 0<r<R and . Indicate expression(s) for the critical point(s) on the sketch.

The capacitance of the arrangement shown in figure is ________ pF

The capacitance of an isolated sphere of radius 10cm in air is equal to ________ pF