Question

The graph below shows the charge on a capacitor as a function of time. The capacitor is connected in series to a resistor and a battery of emf E = 3 V. Note that the charge is measured in millicoulombs (mC). Use the rules of thumb discussed in class and what you know about the charging process in a capacitor to determine the following quantities (write the values only rounded off to zero decimal places) : 1. The time constant for this circuit is ? = __, 2.The capacitance of the capacitor is C = __, 3. The resistance of the resistor is R = __.

Answer 1

The given graph indicates the charging circuit

In charging circuit

Q =Qo(1-e^-t/RC )

if t =Rc

Q =Q0(1-e^-1) =0.63Qo

From grapgh Qo =180 mC

Q =0.63*(180mC) =113.4 mC

We can observe Q =113.4 mC at t = 12 s

t =RC =12 s

1) Time constnat = 12s

2) Qo = 180 mC, Eo =3V

Q =VC

C =Qo/Eo = 0.18/3 = 0.06 F

3) RC =12

R =12/C = 12/0.06 = 200 ohm