Power and energy
- P = V × I (watts)
- P = I² × R
- P = V² / R
- E = P × t (joules when t is in seconds; kilowatt-hours for billing)
Example 1.4. A 12 V motor draws 0.5 A. P = 12 × 0.5 = 6 W. In 2 hours it uses E = 6 × 2 = 12 Wh = 0.012 kWh.
Resistors in series (same current, voltages add): Rtotal = R1 + R2 + R3 + ...
Resistors in parallel (same voltage, currents add): 1 / Rtotal = 1/R1 + 1/R2 + 1/R3 + ... For two resistors: Rtotal = (R1 × R2) / (R1 + R2).
Example 1.5. 100 Ω and 300 Ω in parallel: R = (100 × 300) / 400 = 75 Ω.
Voltage divider (used with many sensors): Vout = Vin × R2 / (R1 + R2)
Example 1.6. Vin = 5 V, R1 = 10 kΩ, R2 = 10 kΩ. Vout = 5 × 10 / 20 = 2.5 V.
Kirchhoff's laws
- KCL (current law): the total current entering a junction equals the total current leaving it.
- KVL (voltage law): the sum of voltage rises equals the sum of voltage drops around any closed loop.