Current Electricity Cheatsheet

Cheat Codes & Shortcuts

• Electric Current: \( I = \frac{dq}{dt} \), rate of flow of charge.
• Ohm’s Law: \( V = IR \), where \( V \) is voltage, \( I \) is current, \( R \) is resistance.
• Resistance: \( R = \frac{\rho L}{A} \), where \( \rho \) is resistivity, \( L \) is length, \( A \) is cross-sectional area.
• Power: \( P = VI = I^2R = \frac{V^2}{R} \).
• Series Circuits: \( R_{\text{eq}} = R_1 + R_2 + \dots \), same current, voltage divides.
• Parallel Circuits: \( \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots \), same voltage, current divides.
• Kirchhoff’s Current Law (KCL): Sum of currents entering a junction equals sum of currents leaving.
• Kirchhoff’s Voltage Law (KVL): Sum of voltage drops around a closed loop equals zero.
• Drift Velocity: \( v_d = \frac{I}{nqA} \), where \( n \) is charge carrier density, \( q \) is charge.
• EMF: Electromotive force, \( \mathcal{E} = V + Ir \), where \( r \) is internal resistance.

Quick Reference Table

Advice

Current Electricity Quick Tips

• Ohm’s Law: Use \( V = IR \) to find missing variables in a circuit.
• Series Circuits: Current is constant; add resistances directly.
• Parallel Circuits: Voltage is constant; add reciprocals of resistances.
• Power Calculation: Use \( P = VI \) or its variants for energy problems.
• Kirchhoff’s Laws: Apply KCL for junctions and KVL for loops in complex circuits.