1. DC Circuits AP Physics Chapter 18

2. DC Circuits 19.1 EMF and Terminal Voltage

3. The Electric Battery EMF – electromotive force – the potential difference between the terminals of a source when no current flows to an external circuit (  ) 19.1

4. The Electric Battery A battery will have an internal resistance (r) So there is a potential drop due to the current that travels through the cell So the actual potential across the terminals of a cell will be This is called the terminal voltage 19.1

5. DC Circuits 19.2 Resistors in Series and in Parallel

6. Resistors in Series and in Parallel When resistors are place in a single pathway They are said to be in series A schematic would look like this 19.2

7. Resistors in Series and in Parallel The current in a series circuit is the same throughout the circuit The potential across the source of EMF is equal to the sum of the potential drops across the resistors 19.2

8. S-123 A 35 cm long wire is hooked to a 1.5 V source. It has a radius of 0.2 mm. If a current of 6 A is measured in the wire, what is its resistance? What is the resistivity of the wire? Birds in Series

9. Resistors in Series and in Parallel Since potential can be defined as We can rewrite the equation for potential as 19.2

10. Resistors in Series and in Parallel When resistors are place in a multiple pathways They are said to be in parallel A schematic would look like this 19.2

11. Resistors in Series and in Parallel The potential difference in a parallel circuit is the same throughout the circuit The current through the source of EMF is equal to the sum of the current through the resistors 19.2

12. Resistors in Series and in Parallel Since current can be defined as We can rewrite the equation for potential as 19.2

13. Resistors in Series and in Parallel Circuits that contain both series and parallel components need to be solved in pieces This circuit contains 20  resistors in series 25  resistors and load series to each other and parallel to the 40  resistor 19.2

14. S-124 Four resistors of 10 , 20 , 5 , and 8  respectively are placed in series to a 12 volt source of EMF. A.What is the total resistance of the circuit? B.What is the total current? C.What is the current through each resistor? D.What is the potential drop across each resistor? World Series Champions Now Married in some Small 3 rd World Countries

15. DC Circuits 19.3 Kirchoff’s Rules

16. Kirchoff’s Rules Circuits that are a little more complex We must use Kirchoff’s rules Gustov Kirchoff They are applications of the laws of conservation of energy and conservation of charge 19.3

17. Kirchoff’s Rules Junction Rule – conservation of charge At any junction, the sum of the currents entering the junction must equal the sum of all the currents leaving the junction 19.3

18. Kirchoff’s Rules Loop Rule – the sum of the changes in potential around any closed pathway of a circuit must be zero For loop 1 19.3

19. Kirchoff’s Rules Steps 1.Label the current in each separate branch with a different subscript (the direction does not matter, if the direction is wrong, the answer will have a negative value) 2.Identify the unknowns and apply V=IR 3.Apply the junction rule (at a in our case) so that each current is in at least one equation 19.3 I1I1 I2I2 I3I3

20. Kirchoff’s Rules Steps 4.Choose a loop direction (clockwise or counterclockwise) 5.Apply the loop rule (again enough equations to include all the currents) a. For a resistor apply Ohm’s law – the value is positive if it goes in the direction of the loop b. For a battery, the value is positive if the loop goes from – to + (nub to big end) 19.3 I1I1 I2I2 I3I3

21. Kirchoff’s Rules Steps We’ll do the two inside loops 6. Combine the equations and solve 19.3 I1I1 I2I2 I3I3

22. S-126 3 10  resistors are placed in a circuit with a 6 volt source of EMF. A.What is the equivalent resistance, potential drop and current if they are in series? B.What if they are in parallel? C.What if two are placed parallel to each other then in series with the third?

23. S-127 What is the the value for each current in the circuit below? R 1 = 1  R 2 = 2  R 3 = 2  R 4 = 1  E 1 = 4 V E 2 = 2 V I1I1 I2I2 I3I3

24. S-129 What is the the value for each current in the circuit below? R 1 = 1  R 2 = 2  R 3 = 2  R 4 = 1  E 1 = 4 V E 2 = 2 V

25. DC Circuits 19.6 RC Circuits-Resistors and Capacitors in Series

26. RC Circuits 19.6 Used windshield wipers timing of traffic lights camera flashes When the switch is closed current flows and potential difference across the capacitor increases

27. RC Circuits 19.6 Eventually the potential difference across the capacitor is equal to the EMF of the battery Current is now zero

28. RC Circuits 19.6 The shape of the curve is given by RC = the time constant Measures how quickly the capacitor becomes charged All circuits have some resistance, so they all take time to charge

30. S-130 A 12  F capacitor is placed in an RC circuit with a single 10  resistor. If the two are placed in series with a 9 V source of EMF and allowed to fully charge A.What is the charge on the capacitor? B.What is the current in the resistor C.How much energy is stored in the capacitor?

31. S-127 Three 12  F capacitor are placed in a circuit across a 6 volt source of EMF. A.What is the charge and potential difference across each capacitor if they are in series? B.What is the charge and potential difference across each capacitor if they are in parallel?

32. S-128 Three 12  F capacitor are placed in a circuit across a 6 volt source of EMF with one in series and the other two parallel to each other. A.What is the equivalent capacitance of the circuit? B.What is the charge and potential drop across each capacitor?

33. S-129 All the resistors are 4 , and each cell is 3 V. What is the current in the center branch? How much power is dissipated by that resistor?

34. S-130 What is the charge and potential drop across each of the following capacitors if they are connected to a 12 V source of EMF?? C 1 = 2  F C 2 = 4  F C 3 = 3  F C 4 = 1  F C 5 = 6  F C 6 = 3  F

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36. S-131 Use Kirchoff’s laws to solve the following problem. Calculate the current through and potential across each resistor. Also calculate the power dissipated in each resistor. V=3V R 1 =5  R 2 =10  R 3 =5  R 4 =5  R 5 =10 

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38. S-132 Happy Test Day