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

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

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

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

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

$\frac{v_o}{v_i}=\frac{1/R_3-1/R_2}{1/R_1+1/R_2}$