Advertisements
Advertisements
प्रश्न
A 100 μF capacitor is joined to a 24 V battery through a 1.0 MΩ resistor. Plot qualitative graphs (a) between current and time for the first 10 minutes and (b) between charge and time for the same period.
Advertisements
उत्तर
Time constant of the circuit,
τ = RC
= 1 × 106 × 100 × 10−6
= 100 s
The growth of charge through a capacitor,
\[q = VC \left(1 - e^{- \frac{t}{RC}}\right)\]
The current through the circuit,
\[i = \frac{dq}{dt}\]
\[ = \frac{VC}{RC} \cdot e^{- \frac{t}{RC}} \]
\[ = \frac{V}{R} . e^{- \frac{t}{RC}} \]
\[ = 24 \times {10}^{- 6} \cdot e^{- \frac{t}{100}}\]
For t = 10 min = 600 s
q = 24 × 10−4 × (1 − e−6)
= 23.99 × 10−4
\[i = \frac{24}{{10}^6} . \frac{1}{e} = 5 . 9 \times {10}^{- 8} A\]
(a) The plot between current and time for the first 10 minutes is shown below.
(b) The plot between charge and time for the first 10 minutes is shown below.
APPEARS IN
संबंधित प्रश्न
A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor?
In the following arrangement of capacitors, the energy stored in the 6 µF capacitor is E. Find the value of the following :
(i) Energy stored in 12 µF capacitor.
(ii) Energy stored in 3 µF capacitor.
(iii) Total energy drawn from the battery.
The energy density in the electric field created by a point charge falls off with the distance from the point charge as
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 current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.
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?
How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?
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.
A capacitor with stored energy 4⋅0 J is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors.
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 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.
A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.
Choose the correct option:
Energy stored in a capacitor and dissipated during charging a capacitor bear a ratio.
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is ______.
An air-filled parallel plate capacitor has a uniform electric field `overset(->)("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 ______
(∈0 = permittivity of free space)
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)
A parallel plate capacitor has a uniform electric field `overset(->)("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)
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.
