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Main » Electricity » Electric Circuits » Lesson III.3.2

### Resistance - Lesson III.3.2

 Key Terms: resistance | equivalent (total) resistance |

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.