85-3 The source-free RC circuit The series combination of a resistor and capacitor has a greater practical importance than does the combination of a resistor and an inductor We shall assume an initial stored energy in the capacitor i(t adu U=0 Let v(t)=Ae-iyr dt R CAse i+-e 0 u(t) R R A(Cs1+)e=0→s R I RC D(0)=Vo ∴U(t)=AeRC U(0)=V0∴A=V o(t)=e RC and i(t) RC R RThe series combination of a resistor and capacitor has a greater practical importance than does the combination of a resistor and an inductor. §5-3 The source-free RC circuit We shall assume an initial stored energy in the capacitor: RC t t Ae − ( ) = 0 0 (0) =V  A =V s t Let t Ae dt R d C 1 + = 0 ( ) =   0 1 1 1 + = s t s t e R A CAs e RC e s R A Cs s t 1 ) 0 1 ( 1 1 1 + = → = − t RC t RC e R V R t t V e and i t 1 0 1 0 ( ) ( ) ( ) − − = = =   0 V0 ( ) = −  − + ( t ) R i(t) C