1. ConcepTest 4.1aSeries Resistors I 9 V Assume that the voltage of the battery is 9 V and that the three resistors are identical. What is the potential difference across each resistor? a) 12 V b) zero c) 3 V d) 4 V e) you need to know the actual value of R

2. equal evenly 3 V drop Since the resistors are all equal, the voltage will drop evenly across the 3 resistors, with 1/3 of 9 V across each one. So we get a 3 V drop across each. ConcepTest 4.1aSeries Resistors I 9 V Assume that the voltage of the battery is 9 V and that the three resistors are identical. What is the potential difference across each resistor? a) 12 V b) zero c) 3 V d) 4 V e) you need to know the actual value of R Follow-up: What would be the potential difference if R=  Follow-up: What would be the potential difference if R= 1 

3. ConcepTest 4.1bSeries Resistors II 12 V R 1 = 4  R 2 = 2  In the circuit below, what is the voltage across ? In the circuit below, what is the voltage across R 1 ? a) 12 V b) zero c) 6 V d) 8 V e) 4 V

4. ConcepTest 4.1bSeries Resistors II 12 V R 1 = 4  R 2 = 2  In the circuit below, what is the voltage across ? In the circuit below, what is the voltage across R 1 ? a) 12 V b) zero c) 6 V d) 8 V e) 4 V The voltage drop across R 1 has to be twice as big as the drop across R 2.V 1 = 8 V The voltage drop across R 1 has to be twice as big as the drop across R 2. This means that V 1 = 8 V and V 2 = 4 V. Or else you could find the current I = V/R = (12 V)/(6  = 2 A, then use Ohm’s Law to get voltages. Follow-up: What happens if the voltage is doubled?

5. ConcepTest 4.2aParallel Resistors I In the circuit below, what is the current through ? In the circuit below, what is the current through R 1 ? 10 V R 1 = 5  R 2 = 2  a) 10 A b) zero c) 5 A d) 2 A e) 7 A

6. voltagesame V 1 = I 1 R 1 I 1 = 2 A The voltage is the same (10 V) across each resistor because they are in parallel. Thus, we can use Ohm’s Law, V 1 = I 1 R 1 to find the current I 1 = 2 A. ConcepTest 4.2aParallel Resistors I In the circuit below, what is the current through ? In the circuit below, what is the current through R 1 ? 10 V R 1 = 5  R 2 = 2  a) 10 A b) zero c) 5 A d) 2 A e) 7 A Follow-up: What is the total current through the battery?

7. ConcepTest 4.2bParallel Resistors II a) increases b) remains the same c) decreases d) drops to zero Points P and Q are connected to a battery of fixed voltage. As more resistors R are added to the parallel circuit, what happens to the total current in the circuit?

8. ConcepTest 4.2bParallel Resistors II a) increases b) remains the same c) decreases d) drops to zero resistance of the circuit drops resistance decreasescurrent must increase As we add parallel resistors, the overall resistance of the circuit drops. Since V = IR, and V is held constant by the battery, when resistance decreases, the current must increase. Points P and Q are connected to a battery of fixed voltage. As more resistors R are added to the parallel circuit, what happens to the total current in the circuit? Follow-up: What happens to the current through each resistor?

9. ConcepTest 4.3aShort Circuit Current flows through a lightbulb. If a wire is now connected across the bulb, what happens? all the current continues to flow through the bulb a) all the current continues to flow through the bulb half the current flows through the wire, the other half continues through the bulb b) half the current flows through the wire, the other half continues through the bulb all the current flows through the wire c) all the current flows through the wire none of the above d) none of the above

10. zeroALL The current divides based on the ratio of the resistances. If one of the resistances is zero, then ALL of the current will flow through that path. ConcepTest 4.3aShort Circuit Current flows through a lightbulb. If a wire is now connected across the bulb, what happens? all the current continues to flow through the bulb a) all the current continues to flow through the bulb half the current flows through the wire, the other half continues through the bulb b) half the current flows through the wire, the other half continues through the bulb all the current flows through the wire c) all the current flows through the wire none of the above d) none of the above Follow-up: Doesn’t the wire have SOME resistance?

11. ConcepTest 4.3bShort Circuit II Two lightbulbs A and B are connected in series to a constant voltage source. When a wire is connected across B, bulb A will: glow brighter than before a) glow brighter than before glow just the same as before b) glow just the same as before glow dimmer than before c) glow dimmer than before d) go out completely e) explode

12. total resistance of the circuit decreasescurrent through bulb A increases Since bulb B is bypassed by the wire, the total resistance of the circuit decreases. This means that the current through bulb A increases. ConcepTest 4.3bShort Circuit II Two lightbulbs A and B are connected in series to a constant voltage source. When a wire is connected across B, bulb A will: glow brighter than before a) glow brighter than before glow just the same as before b) glow just the same as before glow dimmer than before c) glow dimmer than before d) go out completely e) explode Follow-up: What happens to bulb B?

13. ConcepTest 4.4aCircuits I circuit 1 a) circuit 1 circuit 2 b) circuit 2 both the same c) both the same it depends on R d) it depends on R The lightbulbs in the circuit below are identical with the same resistance R. Which circuit produces more light? (brightness  power)

14. ConcepTest 4.4aCircuits I circuit 1 a) circuit 1 circuit 2 b) circuit 2 both the same c) both the same it depends on R d) it depends on R The lightbulbs in the circuit below are identical with the same resistance R. Which circuit produces more light? (brightness  power) parallel lowering the total resistance #1 willdraw a higher current P = I V In #1, the bulbs are in parallel, lowering the total resistance of the circuit. Thus, circuit #1 will draw a higher current, which leads to more light, because P = I V.

15. ConcepTest 4.4bCircuits II twice as much a) twice as much the same b) the same 1/2 as much c) 1/2 as much 1/4 as much d) 1/4 as much 4 times as much e) 4 times as much 10 V A B C The three lightbulbs in the circuit all have the same resistance of 1  By how much is the brightness of bulb B greater or smaller than the brightness of bulb A? (brightness  power)

16. ConcepTest 4.4bCircuits II twice as much a) twice as much the same b) the same 1/2 as much c) 1/2 as much 1/4 as much d) 1/4 as much 4 times as much e) 4 times as much 10 V A B C We can use P = V 2 /R to compare the power: P A = (= 100 W P A = (V A ) 2 /R A = (10 V) 2 /1  = 100 W P B = (= 25 W P B = (V B ) 2 /R B = (5 V) 2 /1  = 25 W The three light bulbs in the circuit all have the same resistance of 1  By how much is the brightness of bulb B greater or smaller than the brightness of bulb A? (brightness  power) Follow-up: What is the total current in the circuit?

17. ConcepTest 4.5aMore Circuits I increase a) increase decrease b) decrease stay the same c) stay the same What happens to the voltage across the resistor R 1 when the switch is closed? The voltage will: V R1R1 R3R3 R2R2 S

18. ConcepTest 4.5aMore Circuits I increase a) increase decrease b) decrease stay the same c) stay the same What happens to the voltage across the resistor R 1 when the switch is closed? The voltage will: decreases the equivalent resistancecurrent from the battery increases increase in the voltage across R 1 With the switch closed, the addition of R 2 to R 3 decreases the equivalent resistance, so the current from the battery increases. This will cause an increase in the voltage across R 1. V R1R1 R3R3 R2R2 S Follow-up: ? Follow-up: What happens to the current through R 3 ?

19. ConcepTest 4.5bMore Circuits II increases a) increases decreases b) decreases stays the same c) stays the same V R1R1 R3R3 R4R4 R2R2 S What happens to the voltage across the resistor R 4 when the switch is closed?

20. V R1R1 R3R3 R4R4 R2R2 S A B C increase in the voltage across R 1 V AB constant V AB increasesV BC must decrease We just saw that closing the switch causes an increase in the voltage across R 1 (which is V AB ). The voltage of the battery is constant, so if V AB increases, then V BC must decrease! What happens to the voltage across the resistor R 4 when the switch is closed? increases a) increases decreases b) decreases stays the same c) stays the same ConcepTest 4.5bMore Circuits II Follow-up: ? Follow-up: What happens to the current through R 4 ?

21. ConcepTest 4.6ircuits ConcepTest 4.6Even More Circuits Which resistor has the greatest current going through it? Assume that all the resistors are equal. V R1R1 R2R2 R3R3 R5R5 R4R4 a) R 1 and b) both R 1 and R 2 equally and c) R 3 and R 4 d) R 5 e) all the same

22. I 1 = I 2 R 5 R 3 + R 4 branch containing R 5 has less resistance The same current must flow through left and right combinations of resistors. On the LEFT, the current splits equally, so I 1 = I 2. On the RIGHT, more current will go through R 5 than R 3 + R 4 since the branch containing R 5 has less resistance. ConcepTest 4.6 ircuits ConcepTest 4.6 Even More Circuits a) R 1 and b) both R 1 and R 2 equally and c) R 3 and R 4 d) R 5 e) all the same Which resistor has the greatest current going through it? Assume that all the resistors are equal. V R1R1 R2R2 R3R3 R5R5 R4R4

23. ConcepTest 4.7Junction Rule ConcepTest 4.7 Junction Rule a) 2 A b) 3 A c) 5 A d) 6 A e) 10 A 5 A 8 A 2 A P What is the current in branch P?

24. red One exiting branch has 2 A other branch (at P) must have 6 A The current entering the junction in red is 8 A, so the current leaving must also be 8 A. One exiting branch has 2 A, so the other branch (at P) must have 6 A. 5 A 8 A 2 A P junction 6 A S a) 2 A b) 3 A c) 5 A d) 6 A e) 10 A What is the current in branch P? ConcepTest 4.7Junction Rule ConcepTest 4.7 Junction Rule

25. ConcepTest 4.9Wheatstone Bridge a) I b) I/2 c) I/3 d) I/4 e) zero An ammeter A is connected between points a and b in the circuit below, in which the four resistors are identical. The current through the ammeter is: I Vab

26. resistors are identical voltage drops are the same potentialsab same Since all resistors are identical, the voltage drops are the same across the upper branch and the lower branch. Thus, the potentials at points a and b are also the same. Therefore, no current flows. ConcepTest 4.9 Wheatstone Bridge a) I b) I/2 c) I/3 d) I/4 e) zero An ammeter A is connected between points a and b in the circuit below, in which the four resistors are identical. The current through the ammeter is: I Vab

27. ConcepTest 4.10Kirchhoff’s Rules ConcepTest 4.10 More Kirchhoff’s Rules 2 V 2  2 V 6 V 4 V 3  1  I1I1 I3I3 I2I2 Which of the equations is valid for the circuit below? a) 2 – I 1 – 2I 2 = 0 b) 2 – 2I 1 – 2I 2 – 4I 3 = 0 c) 2 – I 1 – 4 – 2I 2 = 0 d) I 3 – 4 – 2I 2 + 6 = 0 e) 2 – I 1 – 3I 3 – 6 = 0

28. ConcepTest 4.10 Kirchhoff’s Rules ConcepTest 4.10 More Kirchhoff’s Rules 2 V 2  2 V 6 V 4 V 3  1  I1I1 I3I3 I2I2 Eqn. 3 is valid for the left loop Eqn. 3 is valid for the left loop: The left battery gives +2V, then there is a drop through a 1  resistor with current I 1 flowing. Then we go through the middle battery (but from + to – !), which gives –4V. Finally, there is a drop through a 2  resistor with current I 2. Which of the equations is valid for the circuit below? a) 2 – I 1 – 2I 2 = 0 b) 2 – 2I 1 – 2I 2 – 4I 3 = 0 c) 2 – I 1 – 4 – 2I 2 = 0 d) I 3 – 4 – 2I 2 + 6 = 0 e) 2 – I 1 – 3I 3 – 6 = 0