Common Electrical Formulas for DC Circuits

Basic Circuit Components

• Battery: Provides the voltage.
• Resistor: Limits the current flow.
• Conventional Current: Flows from the positive terminal to the negative terminal of the battery.
• Electron Flow: Opposite to conventional current.

Key Electrical Formulas

Ohm's Law

• Formula: ( V = IR )
  • ( V ): Voltage in volts
  • ( I ): Current in amps
  • ( R ): Resistance in ohms

Power

• Formula:
  • ( P = VI )
  • ( P = I^2R )
  • ( P = \frac{V^2}{R} )
  • ( P ) measured in watts
• Conversions:
  • 1 Horsepower = 746 watts
  • 1 Watt = 1 Joule/second

Electrical Work/Energy

• Formula:
  • Work = Power ( \times ) Time
  • ( Energy = Charge \times Voltage )
• Current: Rate of charge flow, ( I = \frac{Q}{t} )
  • 1 Amp = 1 Coulomb/second

Series Circuits

• Current: Same through all components (( I_T = I_1 = I_2 = I_3 )).
• Total Resistance: ( R_T = R_1 + R_2 + R_3 )
• Voltage Drop: ( V = IR )
  • ( V_1 = I_1R_1 )
  • ( V_2 = I_2R_2 )
  • ( V_3 = I_3R_3 )
• Kirchhoff's Voltage Law: ( V_B = V_1 + V_2 + V_3 )

Parallel Circuits

• Voltage: Same across all components (( V_B = V_1 = V_2 = V_3 )).
• Total Resistance: ( \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} )
• Total Current: ( I_T = I_1 + I_2 + I_3 )
• Kirchhoff's Current Law: The total current entering a junction equals the total current leaving it.

Example Problem: Current Calculation

• Scenario: Calculate unknown current ( I_5 ).
• Given:
  • ( I_1 = 20 ) amps
  • ( I_2 = 18 ) amps
  • ( I_3 = 13 ) amps
  • ( I_4 = 29 ) amps
• Solution:
  • ( I_T = I_1 + I_2 - I_3 - I_4 + I_5 = 0 )
  • Solve for ( I_5 ):
    • If ( I_4 = 29 ), ( I_5 = 4 ) amps towards the junction.

Conclusion

• Common formulas used for analyzing simple DC circuits.
• Kirchhoff's laws are essential for understanding current and voltage distributions.

---

For more practice problems and related content, check out the links provided in the description.