Advertisements
Advertisements
प्रश्न
A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 µC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).
उत्तर
Length of a co-axial cylinder, l = 15 cm = 0.15 m
Radius of outer cylinder, r1 = 1.5 cm = 0.015 m
Radius of inner cylinder, r2 = 1.4 cm = 0.014 m
Charge on the inner cylinder, q = 3.5 µC = 3.5 × 10−6 C
Capacitance of a co-axial cylinder of radii r1 and r2 is given by relation
C = `(2piin_0"l")/log_"e"("r"_1/"r"_2)`
Where,
`in_0` = Permittivity of free space = `8.85 xx 10^-12 "N"^-1 "m"^-2 "C"^2`
∴ C = `(2pi xx 8.85 xx 10^-12 xx 0.15)/(2.3026 log_10(0.15/0.14))`
= `(2pi xx 8.85 xx 10^-12 xx 0.15)/(2.3026 xx 0.0299) = 1.2 xx 10^-10 "F"`
Potential difference of the inner cylinder is given by,
`"V" = "q"/"C"`
= `(3.5 xx 10^-6)/(1.2 xx 10^-10) = 2.92 xx 10^4 "V"`
APPEARS IN
संबंधित प्रश्न
A capacitor 'C', a variable resistor 'R' and a bulb 'B' are connected in series to the ac mains in circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor, keeping resistance R to be the same; (ii) the resistance R is increased keeping the same capacitance?
The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. Determine the charge on each capacitor if the combination is connected to a 100 V supply.
Deduce an expression for equivalent capacitance C when three capacitors C1, C2 and C3 connected in parallel.
Suppose a charge +Q1 is given to the positive plate and a charge −Q2 to the negative plate of a capacitor. What is the "charge on the capacitor"?
Each plate of a parallel plate capacitor has a charge q on it. The capacitor is now connected to a batter. Now,
(a) the facing surfaces of the capacitor have equal and opposite charges
(b) the two plates of the capacitor have equal and opposite charges
(c) the battery supplies equal and opposite charges to the two plates
(d) the outer surfaces of the plates have equal charges
A parallel-plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor.
Find the charges on the four capacitors of capacitances 1 μF, 2 μF, 3 μF and 4 μF shown in the figure.
A capacitor of capacitance 5⋅00 µF is charged to 24⋅0 V and another capacitor of capacitance 6⋅0 µF is charged to 12⋅0 V. (a) Find the energy stored in each capacitor. (b) The positive plate of the first capacitor is now connected to the negative plate of the second and vice versa. Find the new charges on the capacitors. (c) Find the loss of electrostatic energy during the process. (d) Where does this energy go?
A wire of resistance 'R' is cut into 'n' equal parts. These parts are then connected in parallel with each other. The equivalent resistance of the combination is :
The figure shows a network of five capacitors connected to a 100 V supply. Calculate the total energy stored in the network.
The equivalent capacitance of the combination shown in the figure is ______.
In the circuit shown in figure, initially K1 is closed and K2 is open. What are the charges on each capacitors.
Then K1 was opened and K2 was closed (order is important), What will be the charge on each capacitor now? [C = 1µF]
The total charge on the system of capacitors C1 = 1 µF, C2 = 2 µF, C3 = 4 µF and C4 = 3 µF connected in parallel is ______. (Assume a battery of 20 V is connected to the combination)
The capacitors, each of 4 µF are to be connected in such a way that the effective capacitance of the combination is 6 µF. This can be achieved by connecting ______.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. What is the total capacitance of the combination?
