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Kirchhoff’s Rules: Series and Parallel Circuits

Learn the fundamentals of series and parallel circuits, applying Kirchhoff's rules to determine voltage drops and equivalent resistance. Discover how brightness of bulbs varies in circuit configurations.

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Kirchhoff’s Rules: Series and Parallel Circuits

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  1. Physics Mrs. Coyle Series and Parallel Circuits

  2. Kirchhoff’s Rules • Series Circuits • Equivalent Resistance • Voltage Drop Across Resistors • Brightness of Bulbs in a Series Circuit Part I

  3. Series Circuit • There is one current path. • All resistors have the same current.

  4. Recognizing if a circuit is in series.

  5. Remember: Conventional Current • Positive charges are “pumped” by the battery from low to high potential. V>0 • When traversing a resistor with the current, there is a decrease in potential. V<0

  6. 1st Rule: (Junction Theorem): At a junction (node), current in= current out 2nd Rule: (Loop Theorem): In a closed loop the sum of the voltages is zero. Kirchhoff’s Rules

  7. In a series circuit the total voltage drop across the resistors equals the sum of the individual voltages. V = V1 + V2 + V3 Voltage Drop in a Series Circuit

  8. Example 1 • If the battery’s voltage is 12V and the voltage across R1 is 5 V, and across R2 is 4V, find the voltage across R3 . • Answer: 3V

  9. V = V1 + V2 + V3 Using Ohm’s Law: IReq = IR1+IR2 +IR3 Equivalent resistance Req = R1 + R2 + R3 Equivalent ResistanceSeries Circuits

  10. Example 2 • If the battery’s voltage is 12V and R1 = 1Ω R2 = 2Ω R3 = 3Ω • Find the equivalent resistance. • Find the current. • Find the voltage across each resistor. • Answer: 6Ω, 2A, 2V, 4V, 6V

  11. The greater the power actually used by a light bulb, the greater the brightness. Note: the power rating of a light bulb is indicated for a given voltage, at room temperature and the bulb may be in a circuit that does not have that voltage. Remember: Brightness of a Light bulb and Power

  12. P= I V P=I2 R P=V2 / R Remember: POwer

  13. Find the total resistance. • Find the current. • Find the power dissipated in each lamp. • Which light bulb will be the brightest and why? • Find the totalpower. • How does the total power compare to the powers of the individual bulbs. • Ans: 450Ω, 0.027A, 0.18W, 0.036W, 0.109W, 250 Ω, 0.324W Example 3 250Ω 50Ω 12 V 150Ω

  14. Parallel Circuits • Equivalent Resistance • Brightness of Light Bulb • Combination Circuits Part II

  15. There is more than one current path. The voltage across the resistors is the same. Parallel Circuits http://www1.curriculum.edu.au/sciencepd/energy/images/energy_ill112.gif

  16. I = I1 + I2 + I3 V=V1=V2=V3 Using Ohm’s Law: V/Req= V/R1 +V/R2 + V/R3 Equivalent Resistance: 1/Req= 1/R1 +1/R2 + 1/R3 Parallel Circuits

  17. When are parallel circuits used?

  18. Find the Req , I’s. How does Req compare with each R?Ans: 0.55Ω, I= 22A, (12A, 6A, 4A) Example 1 =2Ω 12V =1Ω =3Ω

  19. Why should you not plug in too many appliances in the same outlet in a home? Question

  20. Combination Circuits

  21. Ans: 11 Ω, 1.8A, V1=9V, V2=11V, I2=1.1A, I3=0.7A Example 2: Find the Req, all I’s and V’s =10Ω =5Ω =20V =15Ω

  22. Example 3: Find the Req, Total I and All V’s http://www.eng.cam.ac.uk/DesignOffice/mdp/electric_web/DC/00123.png

  23. Req 1 = 71.4Ω Req 2 = 127.3Ω Req = 198.7Ω I=0.12A V1 = 8.6V V2 = 15.3V Answers:

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