Basic Circuit Equations and Laws

Ohm's and Joule's Laws

NOTE: the symbol "V" ("U" in Europe) is sometimes used to represent voltage instead of "E". In some cases, an author or circuit designer may choose to exclusively use "V" for voltage, never using the symbol "E." Other times the two symbols are used interchangeably, or "E" is used to represent voltage from a power source while "V" is used to represent voltage across a load (voltage "drop").

Kirchhoff's Laws

"The algebraic sum of all voltages in a loop must equal zero."
Kirchhoff's Voltage Law (KVL)

"The algebraic sum of all currents entering and exiting a node must equal zero."
Kirchhoff's Current Law (KCL)

Series Circuit Rules

• Components in a series circuit share the same current. I_total = I₁ = I₂ = . . . I_n
• Total resistance in a series circuit is equal to the sum of the individual resistances, making it greater than any of the individual resistances. R_total = R₁ + R₂ + . . . R_n
• Total voltage in a series circuit is equal to the sum of the individual voltage drops. E_total = E₁ + E₂ + . . . E_n

 

Paralel Circuit Rules

• Components in a parallel circuit share the same voltage. E_total = E₁ = E₂ = . . . E_n
• Total resistance in a parallel circuit is less than any of the individual resistances. R_total = 1 / (1/R₁ + 1/R₂ + . . . 1/R_n)
• Total current in a parallel circuit is equal to the sum of the individual branch currents. I_total = I₁ + I₂ + . . . I_n

 

Series and Parallel Component Equivalent Values

Series and parallel resistances

Series and parallel inductances

Series and Parallel Capacitances

Capacitor Sizing Equation

A formula for capacitance in picofarads using practical dimensions:

Inductor Sizing Equation

Wheeler's formulas for inductance of air core coils which follow are usefull for radio frequency inductors. The following formula for the inductance of a single layer air core solenoid coil is accurate to approximately 1% for 2r/l < 3. The thick coil formula is 1% accurate when the denominator terms are approximately equal. Wheeler's spiral formula is 1% accurate for c>0.2r. While this is a "round wire" formula, it may still be applicable to printed circuit spiral inductors at reduced accuracy.

The inductance in henries of a square printed circuit inductor is given by two formulas where p=q, and p≠q.

The wire table provides "turns per inch" for enamel magnet wire for use with the inductance formulas for coils.

Time Constant Equations

Value of time constant in series RC and RL circuits

Time constant in seconds = RC
Time constant in seconds = L/R

Calculating voltage or current at specified time

Calculating time at specified voltage or current

AC Circuit Equations

Inductive reactance

Capacitive reactance

Impedance in relation to R and X

Z_L = R + jX_L

Z_C = R - jX_C

Ohm's Law for AC

Series and Parallel Impedances

NOTE: All impedances must be calculated in complex number form for these equations to work.

Resonance

NOTE: This equation applies to a non-resistive LC circuit. In circuits containing resistance as well as inductance and capacitance, this equation applies only to series configurations and to parallel configurations where R is very small.

AC power

Decibels