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(Solved): Example 2: Charging of a capacitor through a resistor Let's assume a capacitor intially empty (i.e. ...
Example 2: Charging of a capacitor through a resistor Let's assume a capacitor intially empty (i.e.
v_(C)(0)=0). Now, let's connect this capacitor to dc voltage source
V_(s)through a resistor at
t=0(by closing the switch). In this case, notice that
v_(R)(t)=V_(s)-v_(C)(t), which means a charging current of
(V_(s)-v_(C)(t))/(R)will charge the capacitor. Obviously, this charging current will initially be
V_(s)Rand will decrease as the capacitor is charged (After a long time, charging will stop when
v_(C)(t)will reaches
V_(s)value, which sets the charging current zero). By writing the
KCL, we obtain
(V_(s)-v_(C)(t))/(R)=dv_(C)(t)/(d)t, whose solution is as follows:
where \tau =RC is the time constant. 