1. Ohms Law Mitsuko J. Osugi Physics 409D Winter 2004 UBC Physics Outreach

2. Ohm’s Law Current through an ideal conductor is proportional to the applied voltage –Conductor is also known as a resistor –An ideal conductor is a material whose resistance does not change with temperature For an ohmic device, V = Voltage (Volts = V) I = Current (Amperes = A) R = Resistance (Ohms = Ω)

3. Current and Voltage Defined Electric Current: flow of electrons from the negative terminal to the positive one Conventional Current: (the current in electrical circuits) Flow of current from positive terminal to the negative terminal. Current has units of Amperes (A) is measured using ammeters. Voltage: Energy required to move a charge from one point to another. Think of voltage as what pushes the electrons along in the circuit, and current as a group of electrons that are constantly trying to reach a state of equilibrium. If there is no voltage, electrons don’t move, therefore there is no current. Difference in electrical charge between two points creates difference in potential energy, which causes electrons to flow from an area with lots of electrons (negative terminal) to an area with few electrons (positive terminal), producing an electric current.

4. Linearity of Voltage and Current for Resistors which Obey Ohm’s Law Voltage and current are linear when resistance is held constant.

5. Ohmic Resistors Metals obey Ohm’s Law so long as their temperature is held constant –Their resistance values do not fluctuate with temperature i.e. the resistance for each resistor is a constant Most ohmic resistors will behave non-linearly outside of a given range of temperature, pressure, etc.

6. Ohm’s Law continued

7. The total resistance of a circuit is dependant on the number of resistors in the circuit and their configuration Series Circuit Parallel Circuit

8. Kirchhoff’s Current Law Current into junction = Current leaving junction The amount of current that enters a junction is equivalent to the current that leaves the junction

9. Kirchhoff’s Voltage Law Net Voltage for a circuit = 0 Sum of all voltage drops and voltage rises in a circuit (a closed loop) equals zero

10. Series Circuit Current is constant Why? –Only one path for the current to take –Kirchhoff’s Current Law Voltages through circuit equals zero –Kirchhoff’s Voltage Law

11. Series Equivalent Circuit

12. Experiment 1 One 10Ω resistor connected to the 6V power source (batteries). Add another 10Ω resistor to the circuit in series to the first resistor. Q:What is the equivalent resistance, R? What will happen to the value of the current through each resistor? What will happen to the value of the voltage across each resistor?

13. Experiment 1: What is happening in theory

14. Experiment 1: The actual data In reality, the data we get is not the same as what we get in theory. Why? Because when we calculate numbers in theory, we are dealing with an ideal system. In reality there are sources of error in every aspect, which make our numbers imperfect.

15. Parallel Circuit Voltage is constant Why ? –There are 3 closed loops in the circuit, which means the voltage though each loop is equivalent to the voltage supplied (like in a series circuit) Branch currents add to equal total current

16. Parallel Equivalent Circuits

17. Experiment 2 One 10 ohm resistor connected to the battery. Connect a second 10Ω resistor in parallel to the first one Q:What will the new resistance be? What will happen to the current through each resistor and the voltage across each component of the circuit?

18. Experiment 2: What is happening in theory

19. Experiment 2: The actual data

20. We’ve now looked at how basic electrical circuits work with resistors that obey Ohm’s Law linearly. We understand quantitatively how these resistors work, but lets see qualitatively using light bulbs. Let us also determine if light bulbs also obey Ohm’s Law linearly.

21. The Light Bulb and its Components Has two metal contacts at the base which connect to the ends of an electrical circuit The metal contacts are attached to two stiff wires, which are attached to a thin metal filament. The filament is in the middle of the bulb, held up by a glass mount. The wires and the filament are housed in a glass bulb, which is filled with an inert gas, such as argon.

22. Light bulbs and Power Power dissipated by a bulb relates to the brightness of the bulb. The higher the power, the brighter the bulb. Power is measured in Watts [W] For example, think of the bulbs you use at home. The 100W bulbs are brighter than the 50W bulbs.

23. Experiment 3 One bulb connected to the 6V power source. Add another bulb to the circuit in series. Q: What is the initial current through the circuit? When the second bulb is added, will the bulbs become brighter, dimmer, or not change? We can use Ohm’s Law to approximate what will happen in the circuit:

24. Experiment 3: The qualitative results (with some theory)

25. Experiment 3: Some numbers Let’s see what kind of values we find for the voltage across the light bulbs, and the current through the bulbs.

26. Experiment 4 Have one bulb connected to the 6V power source. Add a second bulb to the circuit in parallel. Q: What is the initial current through the circuit? What happens when the second bulb is added?  We can use Ohm’s Law to approximate what will happen in the circuit:

27. Experiment 4: The qualitative results (with some theory)

28. Experiment 3: Some numbers Let’s see what kind of values we find for the voltage across the light bulbs, and the current through the bulbs.

29. Light bulbs do not obey Ohm’s Law Bulbs are non-linear conductorsBulbs are non-linear conductors (R increases with temperature)

30. As light bulbs warm up, their resistance increases. If the current through them remains constant: They glow slightly dimmer when first plugged in. Why? R increases but I remains constant  P increases Most ohmic resistors will behave non-linearly outside of a given range of temperature, pressure, etc. The filaments of light bulbs are made of Tungsten, which is a very good conductor. It heats up easily.

31. Voltage versus Current for Constant Resistance The light bulb does not have a linear relationship. The resistance of the bulb increases as the temperature of the bulb increases.

32. “Memory Bulbs” Experiment Touch each bulb in succession with the wire, completing the series circuit each time Q:What is going to happen? Pay close attention to what happens to each of the bulbs as I close each circuit.

33. “Memory Bulbs” Continued… Filaments stay hot after having been turned off In series, current through each resistor is constant –smallest resistor (coolest bulb) has least power dissipation, therefore it is the dimmest bulb How did THAT happen?? Temperature of bulbs increases  resistance increases  power dissipation (brightness) of bulbs increases

34. Conclusion Ohmic resistors obey Ohm’s Law Resistance is affected by temperature. The resistance of a conductor increases as its temperature increases. Light bulbs do not obey Ohm’s Law –Tungsten is such a good conductor that their resistance depends on their temperature –As their temperature increases, the power dissipated by the bulb increases i.e. They are brighter when they are hotter