1. Kirchhoff’s Rules Physics 102 Professor Lee Carkner Lecture 14

2. PAL #13 Ohm’s Law  1.5 V battery, 167 A current in 1 m long, 2 mm thick wire  R = V/I = 1.5/167 = 0.00898   R =  (L/A)   = RA/L = (0.00898)(p)(0.001)2/1   = 2.8X10 -8 (  m)  wire is aluminum

3. 3  6  2  5  7  6  1.2  5  7  7.2  12  4.5 

4. Circuit Rules  Series:  Conservation of charge  Current:  Voltage:  Resistors: R eq = R 1 + R 2 + R 3 …  Parallel  Conservation of energy  Current:  Voltage:  Resistance: 1/R eq = 1/R 1 + 1/R 2 + 1/R 3...

5. Kirchhoff’s Junction Rule  The sum of currents entering a junction is equal to the sum of currents leaving it   You need to define a magnitude and a direction for the current in every unique piece of the circuit   You can apply the junction rule to every junction

6. Kirchhoff’s Loop Rule  The sum of the potential differences around a closed loop must be zero   Since you wind up back where you started from all of the changes in energy must cancel out   A loop is any closed path the current can flow through

7. Loop Rule Conventions  The sign of the potential change depends on the direction you traverse the loop  Batteries   When moving from - to + terminal the  V is equal to +   When moving from + to - terminal the  V is equal to –    Resistors   When moving against the current the  V is +IR

8. Using Kirchhoff’s Rules 1.Find junctions and mark with big dot  2.Draw the direction and assign a variable to all currents (I 1, I 2, I 3 … )  3.Use the junction rule for each unique junction 4.Use the loop rule for each loop  5.Solve for each variable via substitution  You need as many equations as you have variables

9. Example  Junction rule:   Loop rule:    If you knew all of the  ’s and R’s you could solve for the I’s R1R1 R2R2 R3R3    2  3 I1I1 I2I2 I3I3 Junction

10. Next Time  Read Ch 19.5-19.8  Homework, Ch. 19, P: 20, 27, 29, 35

11. Ohm’s law can be written R = V/I. This means if V in a circuit is doubled, A)R is halved B)R is doubled C)R is quadrupled D)R stays the same E)R will change, but we can’t tell to what value

12. If the voltage applied to a resistor is doubled, what happens to the current and power? A)Double, double B)Quadruple, quadruple C)Double, quadruple D)Quadruple, double E)We cannot tell from the information given

13. A 100 W light bulb is connected to 120 V household current. What is its resistance? A)1.2  B)100  C)144  D)200  E)12000 

14. Three light bulbs with resistance R 1 = 1 , R 2 = 2  and R 3 = 3  are connected in series to a battery. Which has the largest potential drop across it? A)R 1 B)R 2 C)R 3 D)All have the same potential drop E)It depends on the voltage of the battery

15. A string of Christmas trees lights are connected in series. If one light is removed and replaced with a normal wire, A)The other lights get dimmer B)The other lights get brighter C)The other lights don’t change D)It depends on the current in the wire E)It depends on the voltage across the wire

16. The equivalent resistance of this circuit is: a)0.54  b)1.8  c)4.5  d)33  e)None of the above 3  6  2  5  7 