1. Learning objectives Series Resistances Parallel Resistances
Series-Parallel Resistances

2. Total R Equals the Sum of All Series Resistances
Series Resistance Formulas
The total resistance is the sum of the individual resistances.
RT = R1 + R2 + R3 + R4 + R5 R1 R2 R3 R4 R5

3. Total R Equals the Sum of All Series Resistances
Determining the Total Resistance

4. Series IR Voltage Drops
Fig. 4-5: An example of IR voltage drops V1 and V2 in a series circuit.
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5. Learning objectives Series Resistances Parallel Resistances
Series-Parallel Resistances

6. Series and Parallel
Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current.
Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

7. Series and Parallel Connections
Serial connection
Parallel connection

8. The Applied Voltage VA Is the Same Across Parallel Branches
Fig. 5-1: Example of a parallel circuit with two resistors. (a) Wiring diagram.
(b) Schematic diagram.
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9. Each Branch I Equals VA / R
The current in a parallel circuit equals the voltage applied across the circuit divided by the resistance between the two points where the voltage is applied.
Each path for current in a parallel circuit is called a branch. Each branch current equals V/R where V is the same across all branches.

10. Each Branch I Equals VA / R
Fig. 5-3: Parallel circuit. (a) the current in each parallel branch equals the applied voltage VA divided by each branch resistance R.
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11. Resistance in Parallel
Total Current and Reciprocal Resistance Formulas
The equivalent resistance of a parallel circuit equals the reciprocal of the sum of the reciprocals:
Equivalent resistance also equals the applied voltage divided by the total current: IT VA
REQ =
etc. R1 1 + R2 R3

12. Resistance in Parallel
Determining the Equivalent Resistance
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13. Learning objectives Series Resistances Parallel Resistances
Series-Parallel Resistances

14. Finding RT for Series-Parallel Resistances
Overview of Series-Parallel Circuits
A series-parallel circuit, or combination circuit, combines both series and parallel connections.
Series components form a series string.
Parallel components form a parallel bank.

15. Finding RT for Series-Parallel Resistances
Overview of Series-Parallel Circuits
There are three branches in this
circuit; sections 1 and 2 are series strings. 1 2 3 V

16. Finding RT for Series-Parallel Resistances
Overview of Series-Parallel Circuits 1 2 3 V
There are three series sections in this
circuit; sections 1 and 2 are parallel banks.

17. Finding RT for Series-Parallel Resistances
To find RT for a series-parallel circuit, add the series resistances and combine the parallel resistances.
In this diagram, R1 and R2 are in series, and R3 and R4 are in parallel.
Fig: Schematic diagram of a series-parallel circuit.