05 February, 2007

Series and Parallel Circuits

Series and Parallel Circuits :
Series and parallel electrical circuits are two basic ways of wiring components. The names describe the method of attaching components, that is one after the other or next to each other. It is said that two circuit elements are connected in parallel if the ends of one circuit element are connected directly to the corresponding ends of the other. If the circuit elements are connected end to end, it is said that they are connected in series. A series circuit is one that has a single path for current flow through all of its elements. A parallel circuit is one that requires more than one path for current flow in order to reach all of the circuit elements.



With each of the two basic circuit (series and parallel) configurations, we have specific sets of rules describing voltage, current, and resistance relationships.


series circuits :
  • Voltage drops add to equal total voltage.
  • All components share the same (equal) current.
  • Resistances add to equal total resistance.
parallel circuits :
  • All components share the same (equal) voltage.
  • Branch currents add to equal total current.
  • resistances diminish to equal total resistance.

Resistances in Series :
To find the total resistance of all the components, add the individual resistances of each component:

for components in series with resistances R1, R2, etc. To find the current I use Ohm's law:


To find the voltage across a component with resistance Ri, use Ohm's law again:
Vi = IRi
where I is the current, as calculated above. The components divide the voltage according to their resistances, so, in the case of two resistors, V1/V2=R1/R2.

Resistances in Parallel :
Voltages across components in parallel with each other are the same in magnitude and they also have identical polarities. Hence, the same voltage variable is used for all circuits elements in such a circuit. The total current I is the sum of the currents through the individual loops, found by Ohm's Law. Factoring out the voltage gives

Notation
The parallel property can be represented in equations by two vertical lines (as in geometry) to simplify equations. For two resistors,


Resistors
To find the total resistance of all components, add the reciprocals of the resistances Ri of each component and take the reciprocal of the sum:



To find the current in a component with resistance Ri, use Ohm's law again:
The components divide the current according to their reciprocal resistances, so, in the case of two resistors, I1/I2=R2/R1.

For more information on this visit the following links :

http://utwired.engr.utexas.edu/rgd1/lesson05.cfm

http://utwired.engr.utexas.edu/rgd1/lesson04.cfm

http://www.matter.org.uk/Schools/Content/Resistors/Default.htm --- Practice problems

http://www.allaboutcircuits.com/vol_1/chpt_5/1.html

www.mhhe.com/engcs/electrical/hkd/tutorials/Tut2-1.htm ---- Practice problems

http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Resist/Resist2.html

http://www.analyzethat.net/70_parallel_circuit_analysis.php --- Parallel circuits analysis

http://www.analyzethat.net/71_series_circuit_analysis.php ---- Series circuits analysis

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