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## Theory on resistor in series :

Practical circuits often contain very complicated combinations of resistors therefore it is very useful to have a set of rules for finding the equivalent resistance of some general arrangement of resistors. The circuit below shows the series connection of the resistors and the direction of the current.
Fig .1 current direction and series resistors connection.
Since there is only one path for the current to flow the current through each resistor is the same:
\large I=I_{1}=I_{2}=I_{3}=...=I_{n}
(1)
From the Ohm’s low we know that (
V= I*R
) then:
\large V_{Total}=I_{1}*R_{1}+I_{2}*R_{2}+I_{3}*R_{3}+...+I_{n}*R_{n}
(2)
As we already know that the current throw the circuit is the same than we can rewrite the above equation:
\large V_{Total}= I*(R_{1}+R_{2}+R_{3}+...+R_{n})
(3)
Setting equation (3) and Ohm’s low we get:
\large I*R_{equivalent}=I*(R_{1}+R_{2}+R_{3}+...+R_{n})
(4)
Because the currents on both sides of the equation are the same we can cancel it:
\large R_{equivalent}=R_{1}+R_{2}+R_{3}+...+R_{n}
(5)
In general, the equivalent resistance of n resistors connected in series is the sum of the individual resistances:
\large R_{equivalent}=\sum R_{n}
(6)
Resistance can be also overwritten in terms of conductance since conductance is just the reciprocal of the resistance:
\large \frac{1}{g} = \int \frac{1}{g_{n}}
(7)
Tips and tricks :
– A large resistor in series with a smaller resistor has the resistance of the larger one, roughly.

## Practical Example :

If you don’t see the example below than you should follow this steps:

– In your browser allow Java SE 7.

– Lower you java security settings (Go to Control Panel >> Java >> Security and set the security level to medium) .

– Edit Site List (Go to Control Panel >> Java >> Security and click on Edit Site List… and add eagerlearning.org in the list).

Sorry, you need a Java-enabled browser to see the simulation.
You can see 2 circuits but both of them as we already know are equivalent. Why? as you can see the current and the voltage that flows through both circuits are the same. 1 diagram is showing the current and voltage that is flowing through first circuit. 2 diagram is showing the current and voltage that is flowing through second circuit. If you want to change any resistance value or the input voltage than just double click on the object and insert the desired value.
Last updated on Sat , 08 2014