Talk:QB/a21CircuitsBioInstDC circuits

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

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

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

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

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

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

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

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

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

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

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 $I=I_{0}e^{-t/\tau }$ where $\tau =RC$ is RC time, $Q=\varepsilon C$ and $I_{0}=\varepsilon /R$.

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

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