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  Main Electricity Electric Circuits Lesson III.3.2 Electricity

Resistance - Lesson III.3.2

Key Terms:

resistance | equivalent (total) resistance |IL, CCT, NUM

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

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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

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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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