Ohm's Law and Basic Relations
- V = I * R (voltage equals current times resistance)
- P = V * I = I^2 * R = V^2 / R (power)
- Conductance: G = 1/R (siemens, S)
- Resistance of a wire: R = rho * L / A (rho = resistivity, L = length, A = cross-section area)
Kirchhoff's Laws
- KCL (Current Law): sum of currents entering a node = sum leaving (or total = 0)
- KVL (Voltage Law): sum of voltages around any closed loop = 0
- Apply KCL at nodes and KVL around loops to solve circuit networks
Series and Parallel Circuits
- Resistors in series: R_total = R1 + R2 + R3 + ...
- Resistors in parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
- Two parallel resistors: R_total = (R1 * R2) / (R1 + R2)
- Capacitors in series: 1/C_total = 1/C1 + 1/C2 + ...
- Capacitors in parallel: C_total = C1 + C2 + ...
- Inductors in series: L_total = L1 + L2 + ...
- Inductors in parallel: 1/L_total = 1/L1 + 1/L2 + ...
Thevenin and Norton Equivalents
- Thevenin: V_th = open-circuit voltage at terminals
- R_th = V_th / I_sc (or deactivate sources and find equivalent resistance)
- Norton: I_N = short-circuit current = V_th / R_th
- R_N = R_th (Norton and Thevenin resistances are equal)
- Maximum power transfer: R_load = R_th
AC Circuit Analysis
- Impedance of resistor: Z_R = R
- Impedance of capacitor: Z_C = 1/(j*omega*C) = -j/(omega*C)
- Impedance of inductor: Z_L = j*omega*L
- omega = 2*pi*f (angular frequency)
- V_rms = V_peak / sqrt(2)
- I_rms = I_peak / sqrt(2)
AC Power
- Apparent power: S = V_rms * I_rms (VA)
- Real (active) power: P = S * cos(phi) (watts)
- Reactive power: Q = S * sin(phi) (VAR)
- Power factor: PF = cos(phi) = P/S
- S^2 = P^2 + Q^2 (power triangle)
- Complex power: S = P + jQ