1. Circuits with multiple paths and R’s

2. Circuits with multiple paths and R’s
1. Sum of voltage changes around any loop is zero (energy conservation).
2. Voltage V doesn’t change along the wires.
3. Iin=Iout at any junction (charge conservation)
4. Battery ideally supplies a constant Vbattery . Its current is:
5. Each resistor has to obey: means the voltage difference between the two ends of R.
6. Power It’s conserved…the battery gives it to the loads
Don’t try to generalize beyond these principles.
=Vbattery

3. Resistors in series or parallel
For resistors in series ______ is the same
For resistors in parallel ______ is the same

4. Find the total resistance

5. Finding I’s, V’s for each R
First find Rtot and then I through the battery.
Currents–in = Currents–out at any junction.
The sum of all the V steps across each resistor must add up to the battery voltage, for any path through the resistors.
Ask “For which R can I now find V or I?”

6. Find the current through each R
If the battery voltage is 10 V, find the current through the 4 W resistor
Animate

7. Animate

8. P1. If all the resistors are 2W, and Vbattery = 15 V, the voltage difference across the resistor B is _____ V.
1.5
3.0
6.0
10.0
15.0

9. Demo break: earliest large capacitor
Leyden jar

10. Demo of earliest large capacitor
[In about 1750] Abbe Nollet first sent a discharge from a Leyden jar through a company of 180 soldiers holding hands.  This demonstration was before King Louis XV at Versailles.  The King was both impressed and amused as the soldiers all jumped simultaneously when the circuit was completed.  The King requested that the experiment be repeated in Paris.  In the second demonstration, 700 monks in a line received the same treatment. 

11. Ideas to consider on these conceptual questions. 1
Ideas to consider on these conceptual questions. 1. Sum of voltage changes around any loop is zero (energy conservation). 2. Voltage V doesn’t change along the wires. 3. Iin=Iout at any junction (charge conservation) 4. Battery ideally keeps a constant Vbattery. Its current depends on: 5. Each resistor has to obey: means the voltage difference between the two ends of R. 6. Power . It’s conserved…the battery gives it to the load Check your conclusions with these principles!

12. P2. Assume an ideal battery. When the switch is closed, what changes? A. Vbatt B. Ibatt C. Vbatt and Rtot D. Ibatt and Rtot

13. P2. When the switch is closed the top bulb A. gets brighter B
P2. When the switch is closed the top bulb A. gets brighter B. gets dimmer C. stays the same

14. P7. When a third identical bulb (resistor) is added as shown, which changes? A. DVa B. DVb C. both D. neither
P8. …so
A. a is brighter, b is dimmer
B. a is dimmer, b is brighter
C. a is brighter, b is unchanged
D. a is unchanged, b is dimmer
E. a is unchanged, b is brighter

15. P8. When the wire near b is added in the corner, A
P8. When the wire near b is added in the corner, A. a is brighter, b is dimmer B. a is dimmer, b is brighter. C. a is unchanged, b is dimmer. D. a is brighter, b is unchanged. E. both are unchanged

16. P2. Which voltage difference is greater? A. V1 B. V2 C. the same
P1. If the bulbs and batteries are the same in both pictures, which current is greater? A. I1 B. I2 C. the same I1 V1 V2 I2
P2. Which voltage difference is greater?
A. V1
B. V2
C. the same