As with resistors, voltage source can also be added in Series. Sources can be added in two configuration .

· Series Aiding : Sources that causes the current to flow in same direction

·Series Opposing : Sources that forces current to flow in opposite direction

Sources are normally added to control voltage and current in a circuit .

Series Aiding Sources.

Series aiding sources are those sources which forces current to move in same direction . In the below example , we have two sources. Note that they are producing current in same direction

Observation

Note that both the sources produce current in same direction , as represented by blue arrow

And the +ive terminal is connected to negative terminal of circuit ,

Hence the sources are connected in sources and will voltage will be added

Total voltage = 3+5=8

Series Opposing

In series opposing Current we have sources that forces current to move in different direction

Note in the above mentioned circuit , the current flows in opposite direction .

And the negative terminal of the battery is connected to the other negative terminal

Total Voltage =5-3=2 Volt

Question 1. Find Total Current

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Step 1 . Find Voltage

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Step 2: Find Current

Current = 0.514 Ampere

Question 2 : For the Following circuit , find the voltage dissipated by resistor

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As already discussed the following circuit can be re drawn as

Re labeling the Circuit.

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The Following Formula has been used to calculate the voltage of all resistance .

V=IR

Question 3. For the Following Circuit, Find Vab

Step 1. Labeling the signs

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Writing Equation . (Tip, write down the first sign of every component with voltage, we are starting with R=20 Ohm, which have –ive sign first

-10.28v-5.14V-5V-2.57+Vab=0

=Vab=22.99V