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 $R$ and measured in unit Ohm ${\displaystyle }$ . According to Ohm's law,

$V=IR$

Hence, resistance can be calculated as shown below

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

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

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

From above

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

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

Electricity response of resistor

Resistor and DC electricity

Voltage

$V=IR$

Current

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

Resistance

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

Conductance

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

Resistor and AC electricity

Impedance

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

Reactance

$X=0$

Voltage

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

Current

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

Power generated

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

Magnetic field strength

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

Resistance as a function of temperature

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

Power loss

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

Power provided

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

Resistor circuit

Series resistor circuit

For N resistors connected in series

Total resistance

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

Parallel resistor circuit

For N resistors connected in parallel

Total resistance

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

2 port resistor circuit

For 2 resistors

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

For 3 resistors

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

For 3 resistors

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