Advertisements
Advertisements
Question
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.
Advertisements
Solution
The growth of charge across a capacitor,
`Q=CV(1-e^-t/(RC))`
\[ Q_0 = CV = 20 \times 6 \times {10}^{- 6} C\]
= `20 xx 6 xx 10 ^(-6) (1 - e (- 2 xx (10)^-3)/((10)^2 . 20 xx (10)^-6))`
= `12 xx 10 ^ -5 (1 - e ^ -1)`
= `7.12 xx 0.63 xx 10 ^-5`
= `7.56 xx 10 ^-5`
= `75.6 xx 10 ^-6`
= 76 μc.
APPEARS IN
RELATED QUESTIONS
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
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.
A capacitor of capacitance 500 μF is connected to a battery through a 10 kΩ resistor. The charge stored in the capacitor in the first 5 s is larger than the charge stored in the next.
(a) 5 s
(b) 50 s
(c) 500 s
(d) 500 s
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 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.
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?
By evaluating ∫i2Rdt, show that when a capacitor is charged by connecting it to a battery through a resistor, the energy dissipated as heat equals 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 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.
Obtain the expression for the energy stored in a capacitor connected across a dc battery.
If the p. d. across a capacitor is increased from 10 V to 30 V, then the energy stored with the capacitor ____________.
A capacitor is charged by a battery and energy stored is 'U'. Now the battery is removed and the distance between plates is increased to four times. The energy stored becomes ______.
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 2µF capacitor is charge to 100 volt and then its plate are connected by a conducting wire. The heat produced is:-
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?
If the charge on the parallel plate capacitor is increased by 3 C, the energy stored in it increases by 44%. The original charge on the capacitor is ______.
Evaluating the work integral for charging a capacitor from \(0\) to \(Q\) gives which result?
