# Talk:QB/a21CircuitsBioInstDC circuits

Electric current: 1 Amp (A) = 1 Coulomb (C) per second (s)

Current=${\displaystyle I=dQ/dt=nqv_{d}A}$, where

${\displaystyle (n,q,v_{d},A)}$ = (density, charge, speed, Area)

${\displaystyle I=\int {\vec {J}}\cdot d{\vec {A}}}$ where ${\displaystyle {\vec {J}}=nq{\vec {v}}_{d}}$ =current density.

${\displaystyle {\vec {E}}=\rho {\vec {J}}}$ = electric field where ${\displaystyle \rho }$ = resistivity

${\displaystyle \rho =\rho _{0}\left[1+\alpha (T-T_{0})\right]}$, and ${\displaystyle R=R_{0}\left[1+\alpha \Delta T\right]}$,

where ${\displaystyle R=\rho {\tfrac {L}{A}}}$ is resistance

${\displaystyle V=IR}$ and Power=${\displaystyle P=IV=I^{2}R=V^{2}/R}$

${\displaystyle V_{terminal}=\varepsilon -Ir_{eq}}$ where ${\displaystyle r_{eq}}$=internal resistance and ${\displaystyle \varepsilon }$=emf.

${\displaystyle R_{series}=\sum _{i=1}^{N}R_{i}}$ and ${\displaystyle R_{parallel}^{-1}=\sum _{i=1}^{N}R_{i}^{-1}}$

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

Charging an RC (resistor-capacitor) circuit: ${\displaystyle q(t)=Q\left(1-e^{t/\tau }\right)}$ and ${\displaystyle I=I_{0}e^{-t/\tau }}$ where ${\displaystyle \tau =RC}$ is RC time, ${\displaystyle Q=\varepsilon C}$ and ${\displaystyle I_{0}=\varepsilon /R}$.

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