ความเห็น 13 17 ก.ค. 2553 (23:38) RC_DC_series1
http://www.editgrid.com/explore/user/physicsmatayom/RC_DC_SERIES1
charging capacitor_resistor in series
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\[
\begin{array}{l}
RC\_DC\_series1 \\
1.iR + \frac{Q}{C} = E \\
2.R\frac{{dQ}}{{dt}} + \frac{Q}{C} = E \\
3.\int\limits_0^Q {\frac{{d(EC - Q)}}{{(EC - Q)}}} = - \frac{1}{{RC}}\int\limits_0^t {dt} \\
4.[\ln (EC - Q)]_0^Q = - \frac{1}{{RC}}[t]_0^t \\
5.\ln (EC - Q) - \ln (EC) = - \frac{1}{{RC}}[t - 0] \\
6.\ln \frac{{(EC - Q)}}{{EC}} = - \frac{t}{{RC}} \\
7.Q = EC(1 - e^{( - t/RC)} ) \\
8.V_C = Q/C = E(1 - e^{( - t/RC)} ) \\
9.\lim _{t \to \infty } V_C = Q/C = E \\
10.i = \frac{{dQ}}{{dt}} = \frac{E}{R}.e^{( - t/RC)} \\
11.V_R = iR = E.e^{( - t/RC)} \\
12.V_R + V_C = E \\
\\
\end{array}
\]