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
| Concept | Formula | Description |
|---|---|---|
| Ohm’s Law | \( V = IR \) | Relates voltage, current, and resistance. |
| Resistance | \( R = \frac{\rho L}{A} \) | Depends on material resistivity, length, and area. |
| Power | \( P = VI \) | Rate of energy transfer in a circuit. |
| Series | \( R_{\text{eq}} = R_1 + R_2 \) | Total resistance is sum of individual resistances. |
| Parallel | \( \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \) | Reciprocal of total resistance is sum of reciprocals. |
| KCL | \( \sum I_{\text{in}} = \sum I_{\text{out}} \) | Current entering equals current leaving a junction. |
Advice
First Step: Identify whether the circuit is series, parallel, or a combination.
Use Ohm’s Law: Always start with \( V = IR \) for simple circuits.
Kirchhoff’s Laws: Apply KCL and KVL for complex circuits with multiple loops or junctions.
Check Units: Ensure consistency (e.g., ohms for resistance, amperes for current).
Verify: Double-check calculations by substituting back into original equations.
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.
Current Electricity Speed Quiz
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