Ohm’s Law Mitsuko J. Osugi Physics 409D Winter 2004 UBC Physics Outreach

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)

Current and Voltage Defined Conventional Current: (the current in electrical circuits) Flow of current from positive terminal to the negative terminal. - has units of Amperes (A) and is measured using ammeters. Voltage: Energy required to move a charge from one point to another. - has units of Volts (V) and is measured using voltmeters. 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.

Ohmic Resistors Metals obey Ohm’s Law linearly 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.

Voltage and Current Relationship for Linear Resistors Voltage and current are linear when resistance is held constant.

Ohm’s Law continued

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

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

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

Series Circuit Current is constant Why? – Only one path for the current to take

Series Equivalent Circuit

Parallel Circuit Voltage is constant Why ? – There are 3 closed loops in the circuit

Parallel Equivalent Circuits

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 using the relationship V=IR, but lets see qualitatively using light bulbs.

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.

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.

Bulbs in series experiment One bulb connected to the batteries. Add another bulb to the circuit in series. Q: 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 in theory:

Bulbs in series experiment continued…

Bulbs in parallel experiment One bulb connected to the batteries. Add a second bulb to the circuit in parallel. Q: What happens when the second bulb is added?  We can use Ohm’s Law to approximate what will happen in the circuit:

Bulbs in parallel experiment continued…

Light bulbs are not linear The resistance of light bulbs increases with temperature The resistance of light bulbs increases with temperature The filaments of light bulbs are made of Tungsten, which is a very good conductor. It heats up easily.

As light bulbs warm up, their resistance increases. If the current through them remains constant: They glow slightly dimmer when first plugged in. Why? The bulbs are cooler when first plugged in so their resistance is lower. As they heat up their resistance increases but I remains constant  P increases Most ohmic resistors will behave non-linearly outside of a given range of temperature, pressure, etc.

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.

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

“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

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