Question

7.What's so special about 0.63 and 0.37 in the cases of charging and discharging a capacitor with a Resistor in the circuit? Explain each case?

Answer 1

Kirchhost's loop equation, ov- e - R = 0. Ann => op de = da Q-CV a-cv = - 4 dt integrating a from o tot, and assuming that a=0 an too. we get, I da Q- 2) In (Sem) - >> asev (Ire='cs) = Ro Cemeter)

where, a.ch, on the capee- the of charge growth this equation describes cător. as ao ar when tys. Now, we see that time of time and is called dimeursion At time tot a. Qs Roft te Charging rate depends on the realue of CR at has senne dimeursion of time and constant of the crauit. At time tar, QoQollo Ye) es 0.630. . e determines the time required for the a charging capacitor to rise to 63% of its charge on final walce. 0.639. --76.63 Q. # When the power supply is not connected with the circund as shown in the below figure, then, kirchnert's equation, 'integrating from oto &, and assenning at time +=0, Q- Qo (full charge at time t=0), we get, a = Que /cR

This equation shows that the charge decays exponentially with time. Rate of discharge depends on the time constant T=CR. Att tal, ♡ - Poé' - P = 0.37 % . It is the time required for the charge of a discharging capacitor to fall to 0.37% of its initial value. 0,34 Q.--- -CR