Circuit Analysis
Comprehensive guide to electrical circuit analysis, principles, and techniques.
Ohm's Law
Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points:
V = I × R
Where:
- V = voltage (V)
- I = current (A)
- R = resistance (Ω)
Ohm's Law can be rearranged to solve for current or resistance:
I = V / R
R = V / I
Kirchhoff's Laws
Kirchhoff's laws are fundamental for analyzing electrical circuits:
1. Kirchhoff's Current Law (KCL):
The algebraic sum of all currents entering and leaving a node is zero:
∑I = 0
2. Kirchhoff's Voltage Law (KVL):
The algebraic sum of all voltages around any closed loop in a circuit is zero:
∑V = 0
These laws are based on the conservation of charge and energy, respectively.
AC Circuit Analysis
In AC circuits, impedance is used to describe the opposition to current flow, combining resistance and reactance:
Z = R + jX
Where:
- Z = impedance (Ω)
- R = resistance (Ω)
- X = reactance (Ω)
- j = imaginary unit (√-1)
The impedance of common circuit elements:
- Resistor: Z_R = R
- Inductor: Z_L = jωL
- Capacitor: Z_C = 1/(jωC)
Where:
- ω = angular frequency (rad/s)
- L = inductance (H)
- C = capacitance (F)
Power in AC circuits:
S = P + jQ = V × I*
Where:
- S = apparent power (VA)
- P = real power (W)
- Q = reactive power (VAR)
- V = voltage (V)
- I* = complex conjugate of current (A)