Advertisements
Advertisements
प्रश्न
A sphercial capacitor is made of two conducting spherical shells of radii a and b. The space between the shells is filled with a dielectric of dielectric constant K up to a radius c as shown in figure . Calculate the capacitance.
Advertisements
उत्तर
We have two capacitors: one made by the shells a and c and the other made by the shells b and c.
The capacitance of the capacitor `C_(ac)` is given by
`C_(ac) = (4pi∈_0acK)/((c-a))`
The capacitance of the capacitor `C_(cb)` is given by
`C_(cb) = (4pi∈_0bcK)/(K(b-c)`
The two capacitors are in series; thus, the equivalent capacitance is given by
`1/C = 1/C_(ac) + 1/C_(cb)`
⇒ `1/C = ((c-a))/(4pi∈_0acK) + ((b-c))/(4pi∈_0cb)`
⇒ `1/C = (b(c-a)+Ka(b-c))/(K4pi∈_0abc)`
⇒ `C = (K4pi∈_0abc)/(b(c-a)+Ka(b-c))`
APPEARS IN
संबंधित प्रश्न
Define capacitor reactance. Write its S.I units.
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
As `C = (1/V) Q` , can you say that the capacitance C is proportional to the charge Q?
The equivalent capacitance of the combination shown in the figure is _________ .
Find the equivalent capacitance of the system shown in figure between the points a and b.
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?
A parallel-plate capacitor of capacitance 5 µF is connected to a battery of emf 6 V. The separation between the plates is 2 mm. (a) Find the charge on the positive plate. (b) Find the electric field between the plates. (c) A dielectric slab of thickness 1 mm and dielectric constant 5 is inserted into the gap to occupy the lower half of it. Find the capacitance of the new combination. (d) How much charge has flown through the battery after the slab is inserted?
A parallel-plate capacitor has plate area 100 cm2 and plate separation 1⋅0 cm. A glass plate (dielectric constant 6⋅0) of thickness 6⋅0 mm and an ebonite plate (dielectric constant 4⋅0) are inserted one over the other to fill the space between the plates of the capacitor. Find the new capacitance.
Consider the situation shown in figure. The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period.
The figure show a network of five capacitors connected to a 10V battery. Calculate the charge acquired by the 5μF capacitor.
If the voltage applied on a capacitor is increased from V to 2V, choose the correct conclusion.
Three capacitors are connected in a triangle as shown in the figure. The equivalent capacitance between points A and C is ______.
Define ‘capacitance’. Give its unit.
A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system ______.
When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance ______.
The material filled between the plates of a parallel plate capacitor has a resistivity of 200Ωm. The value of the capacitance of the capacitor is 2 pF. If a potential difference of 40V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is ______.
(given the value of relative permittivity of a material is 50.)
A 5µF capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 µF capacitor If the energy change during the charge redistribution is `"X"/100`J then value of X to the 100 nearest integer is ______.
A leaky parallel plate capacitor is filled completely with a material having dielectric constant K = 5 and electric conductivity σ = 7.4 × 10-12 Ω-1 m-1. If the charge on the plate at the instant t = 0 is q = 8.85 µC, then the leakage current at the instant t = 12 s is ______ × 10-1 µA.
A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V. The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is connected across A. Find the ratio of final charges on A and B.
