Parallel Circuit w/ Loads

1. Parallel Circuit w/ Loads

2. Part 1 - Basic Circuit Laws • Ohm’s Law • George Simon Ohm (1789 - 1854), a German physicist was honored with the recognition of the fundamental law of electronics. Mr. Ohm was not given great status a leader in the scientific world by his contemporaries. His research was done on his off time as a teacher.  • Stated by Mr. Ohm in 1826; Ohm’s law established a mathematical relationship between the three major circuit measurements; voltage, resistance, and current.  • V = I * R

3. Kirchoff's Voltage & Current Laws • Gustav Robert Kirchoff (1824 - 1887), a German physicist, developed two laws for analyzing circuits through experimentation around 1857. The two conclusions, which he developed and became known for, are stated as follows: • 1. Kirchoff's Voltage Law (KVL) – The algebraic sum of the voltage drops across each and all of the resistive loads in a circuit are exactly equal to the original voltage supplied to the circuit. There is no loss or gain of voltage.

4. 2. Kirchoff's Current Law (KCL) - The algebraic sum on the currents at any junction in an electrical circuit is equal to zero. A junction is a point where paths of the circuit come together and are interconnected. More simply stated , all of the current that goes into a junction is equal to all the current that goes out of that junction. There is no extra and none is lost. • Kirchhoff's found out that prior to a branch in a circuit a certain amount of current would begin to flow. The amount of current depended on the total amount of resistance in that circuit. But once the circuit branched into several pathways the current also divided as well.

5. Part 2 – Parallel Circuit Basics • When there are components in a circuit that are connected so that they are located in different branches the components are referred to as connected in Parallel. This differs from components connected in series. Series circuits only have one pathway for current to flow and Parallel circuits have multiple pathways which divide up the current in each path depending on the amount of resistance. the current leaving or returning to the PS follows the main-line and is known as line current.

6. The individual pathways are known as branches and the current flowing through them is known as branch current. Fig. 5 - 6 below shows a simple parallel circuit with three resistors, one in each branch. 

7. Gustav Kirchhoff discovered a law of physics that relates how current is affected when it flows into parallel branches. It states:  • Kirchhoff's Current Law (KCL) - The algebraic sum on the currents at any junction in an electrical circuit is equal to zero. A junction is a point where paths of the circuit come together and are interconnected. More simply stated, all of the current that goes into a junction is equal to all the current that goes out of that junction. There is no extra and none is lost.

8. Three Rules for Parallel Circuits • 1 The same voltage is applied across each individual branch. • 2 The total current is equal to the sum of the individual branch currents. • 3 The total resistance is equal to the applied voltage divided by the total current, and this value is always less than the smallest resistance contained in any one branch.

9. Concept 1 - Finding Total Resistance in a parallel circuit • Look again at the primary factors of Resistance, Voltage, and Current. If the total resistance was needed a DMM would be connected in place of the battery thereby seeing the total circuit. What is the total resistance in fig 5-7? 

11. Most people would say 500, but that's not true. Think about it! if 100 cars had one street to drive on than that one street would be full, but if a second street was added now only 50 cars would drive on each street (less congestion); less resistance. What if a third street were added? Now only 33 cars would drive on each street. As streets are being added the congestion is get better not worse. The same goes in an electrical circuit, the DMM would read a total resistance that would be less that any single branch by itself. The equation shown here will help figure the total resistance in a parallel circuit.

12. So using the values in fig 5-7, we have

13. Concept 2 - Finding main-trunk current • When looking to find main-line (trunk) current there are two methods. • 1) If you know the Total Resistance Rt and Applied Voltage Vt then It can be found by Ohm's Law • It = Vt / Rt

14. 2) If you know the individual current flow in each brand Ir1, Ir2, and Ir3 then you can just find their sum. It = Ir1 +Ir2 + Ir3

15. Concept 3 – Finding total applied voltage • Voltage in a Parallel circuit is stable, it stays the same everywhere you measure. You will notice that there is an unbroken conductor run to each and every branch from the voltage source. Therefore the voltage drop across each branch will be the same as the voltage source.

16. Finding total applied voltage very straight forward. Everywhere you measure voltage it is the same. The same voltage is dropped across each branch as it is across the whole circuit. so... • Vt = Vr1 =Vr2 = Vr3

17. If you don't know any voltage at all Total Applied Voltage can be found, again, by Ohm's Law. • Vt = It * Rt

18. Concept 4 - Finding individual branch current • The current in a Parallel Circuit does change. Referring to fig 5-9, the current at point A is related to the total resistance ( IA = V / Rt ). Whereas the current at point C is related to the resistance in the individual branch ( IC = V / R1). The current at point B is at a place where all of the branches have rejoined and therefore is the same as point A.

19. Review • 1 The same voltage is applied across each individual branch. • 2 The total current is equal to the sum of the individual branch currents. • 3 The equivalent resistance is equal to the applied voltage divided by the total current, and this value is always less than the smallest resistance contained in any one branch.

20. Review Series and Parallel differences • When observing series circuits we see that current stays the same throughout the entire circuit and voltage changed. In Parallel circuits we will see that current will change and voltage will remain constant.

21. 1) A Series circuit has only one pathway for current to flow, a Parallel has many. • 2) Voltage drop is the amount of voltage used to cause electrons to flow through a load. • 3) The voltage in the battery will equal the sum of the voltage drops of all the resistors. • 4) In a parallel circuit the same voltage is applied across all branches • 5) In a parallel circuit the Total resistance of a circuit is always less than any one branch resistance.

22. When observing series circuits we saw that current stayed the same throughout the entire circuit and voltage changed. In Parallel circuits we will see that current will change as it divides among the separate branches and voltage will remain constant throughout the circuit. Kirchhoff found that prior to a branch in a circuit a certain amount of current would begin to flow. The amount of current at that point depended on the total amount of resistance in the circuit. But once the circuit branched into several pathways the current also divided as well, flowing into those branches with relationship to the resistance in that branch. Think about it, electricity or any substance that tends to flow always wants to follow the path of least resistance. So as a circuit branches into small parts the current will try to flow toward the least resistance. If all the branches had the exact same resistance would the current flow equally through each branch? Yes. What would happen if one branch had no resistance and the others had more resistance? All of the electrons would flow through the path with no resistance (aka a Shorted circuit). How much current would return back to the power source after the branches came back together again? Exactly the same amount the circuit started with.