Question

An uncharged capacitor and a resistor are connected in series to a source of emf. If emf=9.00 V, capacitance=21.5 ?F, and resistance=127Ω, find (a) the time constant of the circuit. After 1.30 ms, find (b) the charge on the capacitor, (c) the voltage drop across the capacitor, (d) the voltage drop across the resistor, and (e) the current.

Answer 1

C = 21.5 x 10^(-6) F

R = 127Ohms

a) Time constant = RC= ( 127 Ohms)(21.5 x 10^(-6) F}= 0.0027 seconds

c) V = Vo{1-e^(-t/RC)} = 9 {1- e^ (-0.0013/0.0027)} = 3.44 Volts

b) Q = C Vo { 1- e^(-t/RC) } = 21.5 x 10^(-6) F x 9.00 V { 1- e^(- 1.30 x 10^(-3) sec/ 0.0027sec}

= 0.0001935 x 0.3821 = 7.26 x 10^(-5) C

d) I = V/R = 3.44 V / 127 Ohms = 0.027 amps