Ohm's law
For a conductor under constant physical conditions, current is proportional to voltage. Resistance is the ratio of voltage to current.
V = IR | I = V/R | R = V/I
Series circuits
Components in series carry the same current. The supply voltage is shared across the components. Total resistance is the sum of the individual resistances.
RT = R1 + R2 + R3 + ...
Parallel circuits
Components in parallel have the same voltage across them. Current divides between the branches. Total resistance is lower than the smallest branch resistance.
1/RT = 1/R1 + 1/R2 + ...
Kirchhoff's Current Law (KCL)
The total current entering a junction equals the total current leaving it. This follows from the conservation of electric charge. It is useful when finding branch currents in a circuit.
Kirchhoff's Voltage Law (KVL)
The algebraic sum of voltage rises and drops around a closed loop is zero. This follows from energy conservation. It is useful when analysing series circuits and multi-loop networks.
Voltage and current division
In a series resistor chain, the voltage across a resistor is proportional to its resistance. In a parallel network, branch current depends on branch resistance. These rules help calculate bias and divider networks.
Electrical power
Power in a DC resistive circuit can be found from voltage and current, or from resistance and either voltage or current.
P = VI = I²R = V²/R
Worked example
A 12 V supply is connected to a 4 Ω resistor. Current is 12/4 = 3 A. Power is 12 × 3 = 36 W. The resistor must have a suitable power rating, with a safe margin.