1. Direct Current Circuits
Physics 014
Direct Current
Circuits

2. F P

3. Topics
EMF
Resistors
RC circuits

4. Currents and Resistors
We get resistance by applying a potential difference V between two points and measuring the resultant current i.
(Ohms law)

5. Circuits
To move charges through a resistor we need to establish a potential difference. This is done with an emf device. (A battery)

6. Circuits
emf is an abbreviation for electromotive force

7. Circuits

8. Circuits (emf) is an abbreviation for electromotive force
An ideal emf device has no internal resistance
A real emf device has internal resistance

9. Circuits
How do we calculate the current in a single loop circuit if we know ε & R?

10. Circuits
LOOP RULE: The algebraic sum of the changes in potential encountered in a complete traversal of any loop of a circuit must be zero.

11. Circuits
RESISTANCE RULE: For a move through a resistance in the direction of the current, the change in potential is –iR; in the opposite direction +iR

12. Circuits
RESISTANCE RULE: For a move through a resistance in the direction of the current, the change in potential is –iR; in the opposite direction +iR

13. Circuits
Starting at point a, mentally walk clockwise around the circuit until we are back at point a.

14. Circuits

15. Circuits
Grounding

16. Multiloop circuits
The following is a multiloop circuit. How do we calculate the currents if we know R’s & ε’s.
Loop bcdb
Branch bcd
junction

17. Multiloop circuits
JUNCTION RULE: The sum of the currents entering any junction must be equal to the sum of the currents leaving that junction.

18. Multiloop circuits

19. Circuits
What equations do the rules give us?

20. Multiloop circuits
Loop badb
Loop bdcb
Loop adcba

21. Power
In a circuit, the rate at which energy is transferred from a battery to a device is called power.

22. Power
Arbitrary device

23. Power
In terms of potential, resistance and current.

24. Power
The SI unit for power is the Watt (W).
1 W = (1 V) (1 A)

25. Ammeters and Voltmeters

26. RC circuits
What expressions can be found for resistor-capacitor (RC) combination circuits?

27. RC circuits

28. RC circuits
What expressions can be found for resistor capacitor combination circuits?
Charging the capacitor (a switch)
Discharging the capacitor (b switch)

29. RC circuits
Charging: From the loop rule there, solve a differential equation.
After rearrangement and
plugging in for i

30. RC circuits
Charging: We have the following solution for the differential equation.
solution
From q we can get
these

31. RC circuits
It is useful to define the capacitive time constant

32. RC circuits

33. RC Circuits
Discharging: From the loop rule, we have the same differential equation without the emf term.

34. RC circuits
Discharging: We have the following solution for the differential equation.
solution