Resistors

Resistance

• A measure of how strongly a material opposes current
• $R=\frac{V}{I}$
• Unit is in Ohms $\Omega$

Conductance

• A measure of how easily electricity flows through an electrical element
• The inverse of resistance
• $G=\frac{1}{R}=\frac{I}{V}$
• Measured in Siemens ($S$)

Combining

• Series: $R_{eq}=\sum R_n$
• Parallel: $\frac{1}{R_{eq}}=\sum \frac{1}{R_n}=\sum G_n$
  • Special case when 2 resistors: $R_{eq}=\frac{R_1{R}_2}{R_1+R_2}$

Voltage/Current Divider

• Voltage Divider (for resistors in series): $v_n=i{R}_n=v_s\frac{R_n}{R_{eq}}$
• Current Divider (for resistors in parallel): $i_n=\frac{v}{R_n}=i\frac{R_{eq}}{R_j}$

Short/Open Circuits

• In an open circuit (OC) condition, no current flows to the load and the meaning the resistance is infinite.
• In a short circuit (SC) condition when the switch is closed the resistance is zero offering no resistance to the current.