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).
Advertisements
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?
An electrical technician requires a capacitance of 2 µF in a circuit across a potential difference of 1 kV. A large number of 1 µF capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.
Deduce an expression for equivalent capacitance C when three capacitors C1, C2 and C3 connected in parallel.
Figure 4 below shows a capacitor C, an inductor L and a resistor R, connected in series
to an a.c. supply of 220 V
Calculate:
1) The resonant frequency of the given CLR circuit.
2) Current flowing through·the circuit.
3) Average power consumed by the circuit.
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"?
The following figure shows two capacitors connected in series and joined to a battery. The graph shows the variation in potential as one moves from left to right on the branch containing the capacitors.
The separation between the plates of a charged parallel-plate capacitor is increased. Which of the following quantities will change?
(a) Charge on the capacitor
(b) Potential difference across the capacitor
(c) Energy of the capacitor
(d) Energy density between the plates
The plates of a capacitor are 2⋅00 cm apart. An electron-proton pair is released somewhere in the gap between the plates and it is found that the proton reaches the negative plate at the same time as the electron reaches the positive plate. At what distance from the negative plate was the pair released?
Find the charges on the four capacitors of capacitances 1 μF, 2 μF, 3 μF and 4 μF shown in the figure.
An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by `pi /4` . If element X is a pure resistor of 100Ω ,
(a) name the circuit element Y.
(b) calculate the rms value of current, if rms value of voltage is 141V.
(c) what will happen if the ac source is replaced by a dc source ?
Two parallel plate capacitors X and Y, have the same area of plates and same separation between plates. X has air and Y with dielectric of constant 2, between its plates. They are connected in series to a battery of 12 V. The ratio of electrostatic energy stored in X and Y is ______.
The equivalent capacitance of the combination shown in the figure is ______.
Two charges q1 and q2 are placed at (0, 0, d) and (0, 0, – d) respectively. Find locus of points where the potential a zero.
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)
A capacitor of capacity C1 is charged to the potential of V0. On disconnecting with the battery, it is connected with an uncharged capacitor of capacity C2 as shown in the adjoining figure. Find the ratio of energies before and after the connection of switch S.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. What is the total capacitance of the combination?
