Advertisements
Advertisements
प्रश्न
A parallel-plate capacitor having plate area 25 cm2 and separation 1⋅00 mm is connected to a battery of 6⋅0 V. Calculate the charge flown through the battery. How much work has been done by the battery during the process?
Advertisements
उत्तर
The capacitance of a parallel-plate capacitor is given by `C = (∈_0A)/d`
Here ,
A = Area of the plate
d = Distance between the parallel plates
Given :
A = 25 cm2 = `25 xx 10^-4 "m"^2`
d = 1.00 mm = `1 xx 10^-3 "m"`
Now ,
`C = (∈_0A)/d` = `(8.85 xx 10^-12 xx 25 xx 10^-4)/(1 xx 10^-3)`
= `2.21 xx 10^-11 "F"`
When the battery of voltage 6 V is connected to the capacitor, the charge (Q) that flows from the battery is equal to the amount of the charge that the given capacitor can hold.
⇒ Q = CV
⇒ `Q = 2.21 xx 10^-11 xx 6.0`
= `1.33 xx 10^-10 "C"`
The work done by the battery in charging the capacitor is calculated by taking the product of the magnitude of the charge transferred and the voltage of the battery.
Thus, we get
`W = QV`
= `1.33 xx 10^-10 xx 6.0`
= `8.0 xx 10^-10 J`
Thus , the charge flown through the battery is `1.33 xx 10^-10 "C"` and the work done by the battery is `8.0 xx 10^-10 "J"` .
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?
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.
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).
The plates of a parallel-plate capacitor are given equal positive charges. What will be the potential difference between the plates? What will be the charges on the facing surfaces and on the outer surfaces?
A parallel-plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its negative terminal. Let Q, and Q be the charges appearing on the positive and negative plates respectively.
A parallel-plate capacitor having plate area 20 cm2 and separation between the plates 1⋅00 mm is connected to a battery of 12⋅0 V. The plates are pulled apart to increase the separation to 2⋅0 mm. (a) Calculate the charge flown through the circuit during the process. (b) How much energy is absorbed by the battery during the process? (c) Calculate the stored energy in the electric field before and after the process. (d) Using the expression for the force between the plates, find the work done by the person pulling the plates apart. (e) Show and justify that no heat is produced during this transfer of charge as the separation is increased.
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?
Three capacitors of capacitance `C_1 = 3muf` , `C_2 = 6muf` , `C_3 = 10muf` , are connected to a 10V battery as shown in figure 3 below :
Calculate :
(a) Equivalent capacitance.
(b) Electrostatic potential energy stored in the system
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 ?
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 100 Ω,
(a) name the circuit element Y.
(b) calculate the rms value of current, if rms of voltage is 141 V.
(c) what will happen if the ac source is replaced by a dc source
Capacitors connected in series have ______
The equivalent capacitance of the combination shown in the figure is ______.
The equivalent capacitance of the combination shown in the figure is ______.
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?
In the following circuit, the equivalent capacitance between terminal A and terminal B is:
