This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: • Now, i = dq/dt o dq/dt = ( ξ /R)e t/RC o dq = ( ξ /R)e t/RC dt o I (integral from q to 0) dq = ( ξ /R) I (integral from t to 0) e t/RC Remember that I (integral) eax dx = (1/a) eax o Therefore, q = ( ξ /R)[RC][e t/RC ] (evaluated from t to 0) o q = ξ C [ e t/RC1] Or similarly. .. q(t) = C ξ[ 1 e t/RC ] q(t) = C ξ[ 1 e t/ τ ], where τ is the time constant which equals RC. • See Figure 2814 on page 686 on the text for graphs the above information. Discharging a Capacitor • At t > 0, Kirchoff's rule gives, (q/C)  iR =0. o But since i= dq/dt. .... (q/C) + R(dq/dt) =0 o Or. ... R(dq/dt) = (q/C) o Or. ... dq/q =  (1/RC) dt So, I( integral from q to q max ) dq/d = (1/RC) I (integral from t to 0) dt ln (q/ q max ) = t/RC o q(t) = q max et/RC • d/dt [q(t) = q max et/RC ] oi = dq/dt = q max (1/RC)( et/RC ) o So, i = ( q max /RC)( et/RC ) o i = i o et/RC • See problem 72 from Chapter 28 of the text...
View
Full Document
 Spring '07
 MAHLON,GREGORYDA
 Magnetism, RC Circuits, Trigraph, Electric charge, RC circuit, Kirchhoff's circuit laws, Exponential decay, Gustav Kirchhoff

Click to edit the document details