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 $$$$. According to Ohm's law,
 * $$V = I R$$

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

Resistor and DC electricity
Voltage
 * $$V = I R$$

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
 * $$p_V=\frac{W}{t}=\frac{W}{Q} \frac{Q}{t}=v i$$

Magnetic field strength
 * $$B = \frac{\mu i}{2 \pi r}$$

Resistance as a function of temperature
 * $$R(T)=R_o+nT$$ for conductor . $$R(T)=R_oe^{nT}$$ for semi-conductor

Power loss
 * $$p_R= i^2 R(T) = m C \Delta T$$

Power provided
 * $$p= p_V - p_R $$

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