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.
Explain what would happen if the capacitor given in previous question a 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates,
- While the voltage supply remained connected.
- After the supply was disconnected.
Find the ratio of energy stored in the two configurations if they are both connected to the same source.
A capacitor C1 of capacitance 1 μF and a capacitor C2 of capacitance 2 μF are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at t = 0.
(a) The current in each of the two discharging circuits is zero at t = 0.
(b) The currents in the two discharging circuits at t = 0 are equal but not zero.
(c) The currents in the two discharging circuits at t = 0 are unequal.
(d) C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge.
A capacitance C, a resistance R and an emf ε are connected in series at t = 0. What is the maximum value of (a) the potential difference across the resistor (b) the current in the circuit (c) the potential difference across the capacitor (d) the energy stored in the capacitor (e) the power delivered by the battery and (f) the power converted into heat?
The plates of a capacitor of capacitance 10 μF, charged to 60 μC, are joined together by a wire of resistance 10 Ω at t = 0. Find the charge on the capacitor in the circuit at (a) t = 0 (b) t = 30 μs (c) t = 120 μs and (d) t = 1.0 ms.
A capacitor of capacitance C is connected to a battery of emf ε at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate have this maximum value?
A capacitor of capacitance 12.0 μF is connected to a battery of emf 6.00 V and internal resistance 1.00 Ω through resistanceless leads. 12.0 μs after the connections are made, what will be (a) the current in the circuit (b) the power delivered by the battery (c) the power dissipated in heat and (d) the rate at which the energy stored in the capacitor is increasing?
A capacitor of capacitance 100 μF is connected across a battery of emf 6 V through a resistance of 20 kΩ for 4 s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4 s after the battery is disconnected?
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
A capacitor is a device that stores ____________.
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is ______.
What fraction of the energy drawn from the charging battery is stored in a capacitor?
A parallel plate capacitor has a uniform electric field ‘`vec "E"`’ in the space between the plates. If the distance between the plates is ‘d’ and the area of each plate is ‘A’, the energy stored in the capacitor is ______
(ε0 = permittivity of free space)
Prove that, if an insulated, uncharged conductor is placed near a charged conductor and no other conductors are present, the uncharged body must be intermediate in potential between that of the charged body and that of infinity.
A fully charged capacitor C with initial charge q0 is connected to a coil of self-inductance L at t = 0. The time at which the energy is stored equally between the electric and magnetic fields is ______.
Derive an expression for energy stored in a capacitor.
In a capacitor of capacitance 20 µF, the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, what is the new capacitance?
