Series and Parallel Circuits: Current and Voltage Relationships, Study notes of Law

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Series Circuits

Voltage Relationships: Kirchhoff’s Voltage Law

• Kirchhoff’s Voltage Law
  • The sum of the component voltages in a series circuit must equal the source voltage

• Voltage Characteristics where V S = the source (or total) voltage V n = the voltage across the highest numbered resistor in the circuit Series Circuit Characteristics

Resistors in Series

A series connection has a single path from

the battery, through each circuit element in

turn, then back to the battery.

Resistors in Series

The current through each resistor is the same;

the voltage depends on the resistance. The

sum of the voltage drops across the resistors

equals the battery voltage.

(since V=IR )

Parallel Circuits

Parallel Circuit Characteristics o Parallel Circuit – a circuit that provides more than one current path between any two points

Resistors in Parallel

A parallel connection splits the current, but

the voltage across each resistor is the same:

Resistance in a Parallel Circuit

• Since the voltage of each branch is equal ( V

= V

= V

= V

s

), and…

• The consequence of this is that adding more resistors in parallel, REDUCES Req

By Analogy: Series Vs Parallel

E

I

E R 1

R 2 R 3 I 1 I 2 I 3 R 1 R 2 o The more resistors you add in parallel, the more BRANCHES (hoses) you add. This increases current, thereby reducing overall resistance.