# Electricity/Direct current

## Direct current

Direct current is a current that flows in one direction. The value of the current can change over time. However, the direction does not change over time. The polarity of the current remains the same at every point in time. A direct current can be provided by a voltage source.

${\displaystyle i(t)=I}$

An ideal voltage source is a source of electricity that provides a constant voltage independent of the current that is drawn from the source. The polarity of the voltage source does not change over time. A voltage source is a theoretical device. A real voltage source can deliver a constant voltage when the current that is delivered to a load is within certain boundaries. e.g. a voltage source 24 V / 0-3 A can keep the voltage at 24 V when the delivered current is in between 0 to 3 A.

${\displaystyle v(t)=V}$

o---[- +]---o

## DC and conductor

### Resistor

Voltage by Ohm's law

${\displaystyle V=IR}$

Current

${\displaystyle I={\frac {V}{R}}}$

Resistance

${\displaystyle R={\frac {V}{I}}=\rho {\frac {l}{A}}}$

Conductance

${\displaystyle G={\frac {I}{V}}={\frac {1}{R}}={\frac {1}{\rho }}{\frac {A}{l}}=\sigma {\frac {A}{l}}}$
${\displaystyle }$

Power generated

${\displaystyle P_{V}=IV}$

Power loss . Power is dissipated as heat

${\displaystyle P_{V}=IR(T)}$
${\displaystyle R(T)=R_{o}+nT}$
${\displaystyle R(T)=R_{o}e^{nT}}$

Power transmitted

${\displaystyle P=P_{V}-P_{R}}$

### Capacitor

Charge

${\displaystyle Q=CV}$

Capacitance

${\displaystyle C={\frac {Q}{V}}}$

Voltage

${\displaystyle V={\frac {Q}{C}}={\frac {W}{Q}}}$

Current

${\displaystyle I={\frac {Q}{t}}}$

Power

${\displaystyle P={\frac {W}{t}}={\frac {W}{Q}}{\frac {Q}{t}}=VI}$

Electric field

${\displaystyle E={\frac {V}{d}}}$

### Inductor

Magnetic field intensity

${\displaystyle B=LI}$

Inductance

${\displaystyle L={\frac {B}{I}}}$

Current

${\displaystyle I={\frac {B}{L}}}$