Q64 of 126 Page 198

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.

Concepts/Formulas used:


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 charge is at any t>0 is given by:



Note that is known as time constant.


Given,


Capacitance,


EMF of battery,


Resistance,


Now,






Also,




We know that,



At t = 2.0ms,





Hence, the charge on the capacitor at t = 2.0ms is 76μC.


More from this chapter

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62

A parallel-plate capacitor with plate area 20 cm2 and plate separation 1.0 mm is connected to a battery. The resistance of the circuit is 10 kΩ. Find the time constant of the circuit.

 63

A capacitor of capacitance 10 μF is connected to a battery of emf 2V. It is found that it takes 50 ms for the charge on the capacitor to become 12.6 μC. Find the resistance of the circuit.

 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.


 66

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.