1. Three identical bulbs Three identical light bulbs are connected in the circuit shown. When the power is turned on, and with the switch beside bulb C left open, how will the brightnesses of the bulbs compare? 1. A = B = C 2. A > B > C 3. A > B = C 4. A = B > C 5. B > A > C

2. Three identical bulbs, II When the switch is closed, bulb C will turn on, so it definitely gets brighter. What about bulbs A and B? 1. Both A and B get brighter 2. Both A and B get dimmer 3. Both A and B stay the same 4. A gets brighter while B gets dimmer 5. A gets brighter while B stays the same 6. A gets dimmer while B gets brighter 7. A gets dimmer while B stays the same 8. A stays the same while B gets brighter 9. A stays the same while B gets dimmer

3. Three identical bulbs, II Closing the switch brings C into the circuit - this reduces the overall resistance of the circuit, so the current in the circuit increases.

4. Three identical bulbs, II Closing the switch brings C into the circuit - this reduces the overall resistance of the circuit, so the current in the circuit increases. Increasing the current makes A brighter.

5. Three identical bulbs, II Closing the switch brings C into the circuit - this reduces the overall resistance of the circuit, so the current in the circuit increases. Increasing the current makes A brighter. Because ΔV = IR, the potential difference across bulb A increases.

6. Three identical bulbs, II Closing the switch brings C into the circuit - this reduces the overall resistance of the circuit, so the current in the circuit increases. Increasing the current makes A brighter. Because ΔV = IR, the potential difference across bulb A increases. This decreases the potential difference across B, so its current drops and B gets dimmer.

7. The junction rule A junction is a place where three or more current paths meet. The junction rule: The total current coming into a junction equals the total current going out from a junction. In the picture, a 2 Ω resistor is in parallel with a 3 Ω resistor. A current I comes into the junction before the resistors, splitting into two currents I 2 through the 2 Ω resistor and I 3 through the 3 Ω resistor. The junction rule tells us that I = I 2 + I 3

8. How much current? What fraction of the current, I, passes through the 2 Ω resistor? 1. 1/3 2. 2/5 3. 1/2 4. 3/5 5. 2/3

9. The junction rule The correct answer is 3/5, which we can prove. Let's make our method more general by calling the two resistors R 2 and R 3. Resistors in parallel have the same potential difference across them, so: Combine this with the junction equation: I = I 2 + I 3. Therefore: I 3 = I - I 2. Substitute this into the first expression:

10. Conservation of ? The junction rule is actually a conservation law in disguise. It represents conservation of _________ 1. Energy 2. Momentum 3. Mass 4. Charge 5. Current

11. Conservation of ? The junction rule is actually a conservation law in disguise. It represents conservation of charge. 1. Energy 2. Momentum 3. Mass 4. Charge 5. Current

12. The loop rule The second rule we can apply to a circuit is the loop rule: The sum of all the potential differences around a closed loop equals zero. When a charge goes around a complete loop, returning to its starting point, its potential energy must be the same. Positive charges gain energy when they go through batteries from the - terminal to the + terminal, and give up that energy to resistors as they pass through them. Ski hill analogy: chair lift = battery, skiers = charges, ski trails = resistors.

13. The loop rule Let’s apply the loop rule to the following circuit, to determine the current from the battery.

14. Applying the loop rule We could do either loop, but let’s do this one. Guidelines: going from the – terminal to the + terminal across a battery is a positive ΔV, with a magnitude equal to the battery voltage. going through a resistor in the same direction as the current is a negative ΔV, with a magnitude of I × R going the other way flips the signs

15. Applying the loop rule

16. Conservation of ? The loop rule is actually a conservation law in disguise. It represents conservation of _________ 1. Energy 2. Momentum 3. Mass 4. Charge 5. Current

17. Conservation of ? The loop rule is actually a conservation law in disguise. It represents conservation of energy. 1. Energy 2. Momentum 3. Mass 4. Charge 5. Current