# Electronics Bible/Resistor

Resistor is an electronics device made from a straright wire conductor that has capability to resist current flow .

## Resistance

Resistance represents resistor capability to resist current flow . Resistance has a symbol ${\displaystyle R}$ and measured in unit Ohm . According to Ohm's law,

${\displaystyle V=IR}$

Hence, resistance can be calculated as shown below

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

Resistor can be made from a straight wire conductor that has resistance of

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

From above

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

## Electricity response of resistor

### Resistor and DC electricity

Voltage

${\displaystyle V=IR}$

Current

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

Resistance

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

Conductance

${\displaystyle G={\frac {I}{V}}={\frac {1}{R}}}$

### Resistor and AC electricity

Impedance

${\displaystyle Z={\frac {v}{i}}=R+X_{R}=R\angle 0=R}$

Reactance

${\displaystyle X=0}$

Voltage

${\displaystyle v={\frac {W}{Q}}}$

Current

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

Power generated

${\displaystyle p_{V}={\frac {W}{t}}={\frac {W}{Q}}{\frac {Q}{t}}=vi}$

Magnetic field strength

${\displaystyle B={\frac {\mu i}{2\pi r}}}$

Resistance as a function of temperature

${\displaystyle R(T)=R_{o}+nT}$ for conductor . ${\displaystyle R(T)=R_{o}e^{nT}}$ for semi-condcutor

Power loss

${\displaystyle p_{R}=i^{2}R(T)=mC\Delta T}$

Power provided

${\displaystyle p=p_{V}-p_{R}}$

## Resistor circuit

### Series resistor circuit

For N resitors connected in series

Total resistance

${\displaystyle R_{t}=R_{1}+R_{2}+...+R_{n}}$

### Parallel resistor circuit

For N resitors connected in parallel

Total resistance

${\displaystyle {\frac {1}{R_{t}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+...+{\frac {1}{R_{n}}}}$

### 2 port resistor circuit

For 2 resistors

${\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {R_{2}}{R_{2}+R_{3}}}}$

For 3 resistors

${\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {R_{2}+R_{3}}{R_{2}+R_{1}}}}$

For 3 resistors

${\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {1/R_{3}-1/R_{2}}{1/R_{1}+1/R_{2}}}}$