Question

an initially uncharged 1000-nf capacitor is charged by a 12v battery through a resistance R . the capacitor reaches a charge of 4000 nc in a period of 2 s after the charging began. find the value of R and current through the R

Answer 1

Given

capacitance of the capacitor is C = 1000 nF

battery of voltage is V = 12 V ,

resistance R = ?

the charge across the capacitor after 2 s is Q(2s) = 4000 nC

from the relations between Q,C,V ; Q = C*V

total charge of the capacitor it can store or maximum chargeis

   Q = 1000*10^-9 F*12 V = 1.2*10^-5 C

from charging condition of a capacitor in RC circuit is

   q(t) = Q0 (1-e^(-t/T))
T is time constant of RC circuit

susbtituting the values

   4000*10^-9 = (1.2*10^-5)(1-e^(-2/T))

solving for T , T = 4.9326 s
   now T = R*C ==> R = T/C = (4.9326)/(1000*10^-9) ohm = 4932600 ohm

   R = 4.932600*10^6 ohms