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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, It.
- 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, Vt
- Factor out Vt 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 Rt.
- Draw a circle around the parallel connection and determine its resistance.
- Determine Rt for the entire circuit.
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