Q81 of 126 Page 198

A capacitor of capacitance 100 μF is connected across a battery of emf 6.0 V through a resistance of 20 kΩ for 4.0 s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4.0 s after the battery is disconnected?

Concepts/Formulas used:


Charging a capacitor:


A capacitor of capacitance C is connected in series with a resistor of resistance R, a switch, and battery of emf ϵ . It is uncharged at first. The switch is closed at t = 0, then at time any time t the charge stored on the capacitor is given by



Discharging a capacitor:


A capacitor of capacitance C is connected in series with a resistor of resistance R and a switch. Before the switch is closed, it has charge Qi . If the switch is closed at t = 0, then at any time t, the charge on the capacitor is given by:



Given,


Emf = 6V


Capacitance,


Resistance,


Time for charging = time for discharging =


When charging,





When discharging,






Now,


Hence,


More from this chapter

All 126 →
79

Find the charge on each of the capacitors 0.20 ms after the switch S is closed in figure.


 80

The switch S shown in figure is kept closed for a long time and is then opened at t = 0. Find the current in the middle 10 Ω resistor at t = 1.0 ms.


Concepts/Formulas used:


When is capacitor is discharging through as resistor of resistance R, the current through the resistor is given by:



where I0 is the initial current and C is the capacitance of the capacitor.


 82

Consider the situation shown in figure. The switch is closed at t = 0 when the capacitors are uncharged. Find the charge on the capacitor C1 as a function of time t.


 83

A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.