Current

• $1\mathrm{A}=1\frac{\mathrm{C}}{\mathrm{S}}$
• $I=\frac{\mathrm{d}Q}{\mathrm{d}t}$, where $Q$ is Charge
  • The Derivative of Charge wrt time
• use $i=\frac{\mathrm{d}q}{\mathrm{d}t}$ for time varying current
• To find charge at some time given a current, integrate:
  • $$$$

\mathrm{d}q & =i\mathrm{d}t' \
\int_{q(t_{0})}^{q(t)} , dq & =\int_{t_{0}}^{t} i , dt' \
q(t)-q(t_{0}) & =\int_{t_{0}}^{t} i , dt' \
q(t) & =\int_{t_{0}}^{t} i , dt' +q(t_{0})
\end