Electricity - Formula Sheet

Core Formulas of Electricity

The following are the key equations from the Electricity chapter, with all physical symbols defined:

1. Electric Current

\\[I = \\frac{Q}{t}\\]

\n
• I: Electric current in Amperes (A)
\n
• Q: Net charge flowing through the conductor in Coulombs (C)
\n
• t: Time interval in seconds (s)
\n

2. Electric Potential Difference

\\[V = \\frac{W}{Q}\\]

\n
• V: Potential difference in Volts (V)
\n
• W: Work done in moving the charge in Joules (J)
\n
• Q: Quantity of charge in Coulombs (C)
\n

3. Ohm's Law and Resistance

\\[V = I R \\quad \\text{or} \\quad R = \\frac{V}{I}\\]

\n
• V: Potential difference across the ends of the conductor in Volts (V)
\n
• I: Current flowing through the conductor in Amperes (A)
\n
• R: Electrical resistance of the conductor in Ohms (Ω)
\n

4. Electrical Resistivity and Conductivity

\\[\\rho = \\frac{R A}{L} \\quad \\text{and} \\quad \\sigma = \\frac{1}{\\rho}\\]

\n
• ρ (rho): Electrical resistivity (specific resistance) of the material in Ohm-meters (Ω·m)
\n
• σ (sigma): Electrical conductivity of the material in mho-meters^-1 (Ω^-1·m^-1)
\n
• R: Resistance of the wire in Ohms (Ω)
\n
• A: Cross-sectional area of the wire in square meters (m²)
\n
• L: Length of the conducting wire in meters (m)
\n

5. Electrical Conductance

\\[G = \\frac{1}{R}\\]

\n
• G: Conductance of the material in mho or Siemens (S or Ω^-1)
\n
• R: Electrical resistance in Ohms (Ω)
\n

6. Equivalent Resistance in Series

\\[R_s = R_1 + R_2 + R_3\\]

\n
• R_s: Effective resistance of the series combination in Ohms (Ω)
\n
• R₁, R₂, R₃: Resistances of the individual resistors in Ohms (Ω)
\n

7. Equivalent Resistance in Parallel

\\[\\frac{1}{R_p} = \\frac{1}{R_1} + \\frac{1}{R_2} + \\frac{1}{R_3}\\]

\n
• R_p: Effective resistance of the parallel combination in Ohms (Ω)
\n
• R₁, R₂, R₃: Resistances of individual parallel resistors in Ohms (Ω)
\n

8. Joule's Law of Heating

\\[H = I^2 R t = V I t = \\frac{V^2}{R} t\\]

\n
• H: Thermal energy generated in the resistor in Joules (J)
\n
• I: Electric current in Amperes (A)
\n
• R: Resistance in Ohms (Ω)
\n
• V: Potential difference across the resistor in Volts (V)
\n
• t: Time period for which the current passes in seconds (s)
\n

9. Electric Power

\\[P = V I = I^2 R = \\frac{V^2}{R}\\]

\n
• P: Electric power consumed in Watts (W)
\n
• V: Potential difference across the device in Volts (V)
\n
• I: Current flowing through the device in Amperes (A)
\n
• R: Operating resistance of the device in Ohms (Ω)
\n

10. Consumed Electrical Energy

\\[E = P \\times t\\]

\n
• E: Consumed electrical energy in Watt-hours (Wh) or Kilowatt-hours (kWh)
\n
• P: Power rating of the appliance in Watts (W) or Kilowatts (kW)
\n
• t: Continuous duration of usage in hours (h)
\n

11. Mechanical to Electrical Power Conversion

\\[1 \\text{ hp} = 746 \\text{ W}\\]

\n
• hp: Horsepower, a unit in the foot-pound-second (fps) English system used to express power
\n
• W: Watt, the SI unit of power
\n