2026-05-19 06:44

Status: #new

Tags: #physics #electromagnetism

4.3 Conductivity, Kirchhoff's Laws and Power

Conductivity And Resistivity*

• Ohmic Material - A material than maintains a constant resistance
• Resistivity ($\rho$) - The ability for a material to resist electric current
• Conductivity ($\sigma$) - Materials ability to "conduct" electric current
• Resistance (R) - How much an object opposes electric current

Connecting Resistance, Resistivity and Conductivity

• Resistivity and Conductivity are inversely proportional
  • $\to \sigma =\frac{1}{\rho },\rho =\frac{1}{\sigma }$
• Resistance Formula
  • $R=\rho \frac{L}{A}$, where L and A are defined as Length and Area
    

Kirchhoff's Current Law

• The sum of all current ($I$) IN is the same as the current OUT
• $\sum I_{in}=\sum I_{out}$
• Illustration:
  

Kirchhoff's Voltage Law

• The "drop" in voltage is such that the "rise" in voltage minus the "drop" in voltage is equal to 0
• $\sum V_{rise}-\sum V_{drop}=0$, $\sum _{loop}{V}_i=0$
• Illustration:
  

Electric Power

• As current flows through a resistor, there is a net decrease in the Voltage, where the change in electrical potential energy increases thermal energy
• Illustration:
  
• Formulas:
• $P=\frac{E}{T}\to P=\frac{a(V_2-V_1)}{t}=I\mathrm{\Delta }V=I^{2}R\mathrm{or}\frac{(\mathrm{\Delta }V{)}^2}{R}$ , (Change in Volts is Voltage by definition, you can think of $\mathrm{\Delta }V$ as just V)

Cost of Power

• Cost = $P(kW)\cdot t(h)\cdot rate(\frac{cost}{kWh})$
• Convert watts to kW, use hours, and the units should cancel out kWh...

References

4.3 Voltage, Current and Ohms Law
4.0 Electrical Charge
4.2 Electrical Potential