OpenStax University Physics/E&M/Direct-Current Circuits

For quiz at QB/d_cp2.10
$$V_{terminal}=\varepsilon -Ir_{eq}$$ where $$r_{eq}$$=internal resistance and $$\varepsilon$$=emf.

$$R_{series}=\sum_{i=1}^N R_i$$ and $$ R_{parallel}^{-1}=\sum_{i=1}^NR_{i}^{-1}$$

Kirchhoff Junction:$$\sum I_{in}=\sum I_{out}$$ and Loop: $$\sum V = 0$$

Charging an RC (resistor-capacitor) circuit: $$ q(t)=Q\left(1-e^{t/\tau}\right)$$ and $$ I=I_0e^{-t/\tau}$$ where $$\tau = RC$$ is RC time, $$ Q=\varepsilon C$$ and $$I_0=\varepsilon/R$$.

Discharging an RC circuit: $$q(t)=Qe^{-t/\tau}$$ and $$I(t)=-\tfrac{Q}{RC}e^{-t/\tau}$$