An equivalent or total resistance can be considered to consist of a single resistance, which replaces two or more resistances.
Relationships to determine the total resistance in a series or parallel circuit can be developed using Ohm's Law and Kirchhoff's Laws.
Series
 Kirchhoff's Voltage Law for a series circuit states
 Using Ohm's Law V = IR, substitute for V.
 Kirchhoff's Current Law states that in a series circuit, current is equal. We can therefore give all current values the same symbol, I_{t}.
 Factor out It and cancel.
Therefore, to determine total resistance in a series circuit the relationship is …
Parallel
 Kirchhoff's Current Law for a parallel circuit states
 Using Ohm's Law V = IR, substitute for I.
 Kirchhoff's Voltage Law states
and we can therefore give all potential differences the same symbol, V_{t}
 Factor out V_{t} and cancel.
Therefore, to determine total resistance in a parallel circuit the relationship is …
Note: If all resistors have the same value, R, and there are N number of resistors, the total resistance can be calculated using .
Resistance can also be calculated in a circuit, which is a combination of a series and a parallel connection. If the circuit is complex, it is important to break it into simpler parts. One way to achieve this is to draw a circle around part of the circuit. After the part inside the circle is analyzed, another part can be simplified.
For example:
Find R_{t}.
 Draw a circle around the parallel connection and determine its resistance.
 Determine R_{t} for the entire circuit.
