Key Equations

Key Equations

Terminal voltage of a single voltage source	$V_{\text{terminal}}=\epsilon -I{r}_{\text{eq}}$
Equivalent resistance of a series circuit	$R_{\text{eq}}=R_1+R_2+R_3+\text{⋯}+R_{N-1}+R_N={\displaystyle \sum _{i=1}^N{R}_i}$
Equivalent resistance of a parallel circuit	$R_{\text{eq}}={\left(\frac{1}{R_1}+\frac{1}{R2}+\text{⋯}+\frac{1}{R_N}\right)}^{\mathrm{-1}}={\left({\displaystyle \sum _{i=1}^N\frac{1}{R_i}}\right)}^{\mathrm{-1}}$
Junction rule	${\displaystyle \sum I_{\text{in}}={\displaystyle \sum I_{\text{out}}}}$
Loop rule	${\displaystyle \sum V}=0$
Terminal voltage of N voltage sources in series	$V_{\text{terminal}}={\displaystyle \sum _{i=1}^N{\epsilon }_i-I{\displaystyle \sum _{i=1}^N{r}_i}}={\displaystyle \sum _{i=1}^N{\epsilon }_i-I{r}_{\text{eq}}}$
Terminal voltage of N voltage sources in parallel	$V_{\text{terminal}}=\epsilon -I{{\displaystyle \sum _{i=1}^N\left(\frac{1}{r_i}\right)}}^{\mathrm{-1}}=\epsilon -I{r}_{\text{eq}}$
Charge on a charging capacitor	$q\left(t\right)=C\epsilon \left(1-e^{-\frac{t}{RC}}\right)=Q\left(1-e^{-\frac{t}{\tau }}\right)$
Time constant	$\tau =RC$
Current during charging of a capacitor	$I=\frac{\epsilon }{R}{e}^{-\frac{t}{RC}}=I_o{e}^{-\frac{t}{RC}}$
Charge on a discharging capacitor	$q\left(t\right)=Q{e}^{-\frac{t}{\tau }}$
Current during discharging of a capacitor	$I\left(t\right)=-\frac{Q}{RC}{e}^{-\frac{t}{\tau }}$