Q66 of 126 Page 198

A capacitor of capacitance 8.0 μF is connected to a battery of emf 6.0 V through a resistance of 24Ω. Find the current in the circuit

(a) just after the connections are made and


(b) one time constant after the connections are made.


Charging a capacitor:


A capacitor of capacitance C is being charged using a battery of emf ϵ through a resistance R . A switch S is also connected in series with the capacitor. The switch is initially open. The capacitor is uncharged at first. At t=0, the switch is closed. The current through the circuit at anytime t>0 is given by:



Where I0 is the initial current and is the time constant.


Given,


Capacitance,


EMF of battery,


Resistance,


(a)


Just after the connections are made, there is no potential difference across the capacitor and it acts as a short circuit; hence, the current can simply be calculated form Ohm’s law:





(b)


We know that,



Now, at t=τ,




Using the result from (a), we get,



More from this chapter

All 126 →
64

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.

 65

The plates of a capacitor of capacitance 10 μF, charged to 60 μC, are joined together by a wire of resistance 10Ω 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.


 67

A parallel-plate capacitor of plate area 40 cm2 and separation between the plates 0.10 mm is connected to a battery of emf 2.0 V through a 16 Ω resistor. Find the electric field in the capacitor 10 ns after the connections are made.

 68

A parallel-plate capacitor has plate area 20 cm2, plate separation 1.0 mm and a dielectric slab of dielectric constant 5.0 filling up the space between the plates. This capacitor is joined to a battery of emf 6.0 V through a 100 kΩ resistor. Find the energy for the capacitor 8.9 μs after the connections are made.