Question

A 10 ohm resistor and 10 microfarad capacitor are attached in series to a 10 volt DC supply. If the current i(0)=1 ampere, what is the current after 0.1 milliseconds (0.0001 seconds)? Round in the thousandths place.

Answer 1

\[U=u_R+u_C\]\[0=\frac{du_R}{dt}+\frac{du_C}{dt}=R\frac{di}{dt}+\frac{i}{C}\]\[\frac{di}{dt}+\frac{i}{RC}=0\quad,\quad\tau=RC=10\Omega\cdot10\mu F=100\mu s=0.1ms\]\[i(t)=i(0)\exp(-t/\tau)\]\[i(t=0.1ms)=i(0)\exp(-1)=\frac{1}{e}A=0.369\,A\]