Advertisements
Advertisements
प्रश्न
A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an ideal battery of emf ε through a resistance R. Find the charge on the capacitor at time t.
Advertisements
उत्तर
Given:-
Initial charge given to the capacitor = Q
When the capacitor is connected to a battery, it will charge through the battery. The initial charge will also decay.
The growth of charge across the capacitor due to the battery of emf E,
\[q = CE\left( 1 - e^{- \frac{t}{RC}} \right)\]
The decay of charge through the capacitor,
\[q' = Q e^{- \frac{t}{RC}}\]
The net charge on the capacitor at any time t,
\[q_{net} = q + q'\]
\[ = CE\left( 1 - e^{- \frac{t}{RC}} \right) + Q e^{- \frac{t}{RC}}\]
APPEARS IN
संबंधित प्रश्न
Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.
The energy density in the electric field created by a point charge falls off with the distance from the point charge as
(a) Find the current in the 20 Ω resistor shown in the figure. (b) If a capacitor of capacitance 4 μF is joined between the points A and B, what would be the electrostatic energy stored in it in steady state?
A 20 μF capacitor is joined to a battery of emf 6.0 V through a resistance of 100 Ω. Find the charge on the capacitor 2.0 ms after the connections are made.
How many time constants will elapse before the charge on a capacitors falls to 0.1% of its maximum value in a discharging RC circuit?
Two capacitors of capacitances 4⋅0 µF and 6⋅0 µF are connected in series with a battery of 20 V. Find the energy supplied by the battery.
A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating ∫ i2R dt and also by finding the decrease in the energy stored in the capacitor.
Each capacitor in figure has a capacitance of 10 µF. The emf of the battery is 100 V. Find the energy stored in each of the four capacitors.
A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.
A metal sphere of radius R is charged to a potential V.
- Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R.
- Show that the electrostatic field energy stored outside the sphere of radius 2 R equals that stored within it.
A large conducting plane has a surface charge density `1.0 xx 10^-4 "Cm"^-2` . Find the electrostatic energy stored in a cubical volume of edge 1⋅0 cm in front of the plane.
Obtain the expression for the energy stored in a capacitor connected across a dc battery. Hence define energy density of the capacitor
If the p. d. across a capacitor is increased from 10 V to 30 V, then the energy stored with the capacitor ____________.
Do free electrons travel to region of higher potential or lower potential?
Electrostatic energy of 4 x 10−4 J is stored in a charged 25 pF capacitor. Find the charge on the capacitor.
Derive an expression for energy stored in a capacitor.
