3 a At t 0 an uncharged capacitor of capacitance C is connec

3. (a) At t 0, an uncharged capacitor of capacitance C is connected through a resistance R to a battery of con- stant emf (Figure 28.50). (a) How long does it take for the capacitor to reach one half of its final charge? (b) How long does it take for the capacitor to become fully charged? Close at t-0 Figure 28.50

Solution

a) the formula for RC circuit and charge in capacitor is

q = q_o (1-e^{t/RC )}

for 50% charge

Put q= q_o /2 , and we will get

=>1/2 = 1 - e^-t/RC

^=>e^-t/RC = 1/2

^=> -t/ RC = ln 1/2

=> t = RC ln 2

b) For complete charge

Put q = qo , and we will get

=> 1 = 1 - e^-t/RC

So in reality the capacitor never becomes 100% charges as t is edging to infinity here in this equation.