Last Updated: Fri Sep 27 10:15:33 AM CDT 2024

Quiz

• Blackboard

Current

• Current is just charge that moves.
• Current has units of coulombs per second, so we could write it as the derivative of charge.

OR

Resistors

• Resistors resist current

plinko boards do a similar thing for balls.

Demo: Current through a resistor

Let’s run some current through some resistors…

• how much current should we get?

Resistors

• Resistors resist current
• They also dissipate power

plinko boards do a similar thing for balls.

Electric potential in a circuit

At every point in a circuit, we can measure the electric poetential with respect to ground.

Dissipated Power

Resistors dissipate electrical power.

The power is either converted to heat, or work, or both.

The power comes from the potential energy of the charge.

Phone Batteries

• Phones have batteries.
• Battery capacities are typically reported in units of mAh (milliAmpere-hour)
• This is the amount of charge in a milliAmpere current that runs for 1 hour.

Example:

• How much charge does a phone battery move through the phone?
• How much current does a cell phone draw (on average)?
• What is the resistance of a cell phone (most phones use a lithium-ion battery)?
• How much power does a cell phone use (on average)?
• How much energy is used the phone during a single charge?
• How long does it take to recharge the battery?

Phone Batteries

What is the effective resistance of your phone?

(Old) Light Bulb Examples

• Light bulbs are resistors that convert electrical energy into heat/light.

• Incandescent bulbs have a thin wire made of tungsten called a filament.

• The filament gets hot and gives off blackbody radiation

  

(Old) Light Bulb Examples

What is the resistance of a 60 W light bulb

• According to Wikipedia:
  • A typical 60 W light bulb has a tungsten filament that:
    • will uncoil to about 580 mm.
    • The filament diameter is about 0.05 mm.
• According to the text book:
  • Tungsten has a resistivity of \(5.6 \times 10^{-8} \;\Omega \text{m}\)

Resistivity

The resistance of a cylinder is

\(R = \frac{\rho L}{A}\)

\(\rho\) is called the resistivity. It is a property of the material.

The resistivity for most materials depends on its temperature. For metals, resistivity goes up with temperature.

\(\rho = \rho_0 ( 1 + \alpha \Delta T )\)

(Old) Light Bulb Examples

What is the resistance of a 60 W light bulb

• According to Wikipedia:
  • A typical 60 W light bulb has a tungsten filament that:
    • will uncoil to about 580 mm.
    • The filament diameter is about 0.05 mm.
• According to the text book:
  • Tungsten has a resistivity of \(5.6 \times 10^{-8} \;\Omega \text{m}\)

(Old) Light Bulb Examples

What is the temperature of the filament in a 60 W light bulb?

A 60 W light bulb dissipates 60 W of power.

• The light bulb produces light by heating up the filament.
• The resistance of the light bulb increases with temperature.

(Old) Light Bulb Examples

How much current runs through a 60 W light bulb?

A 60 W light bulb dissipates 60 W of power.

The voltage applied to the light bulb is 120 V (in the US)

(Old) Light Bulb Examples

How much current runs through a 60 W light bulb?

A 60 W light bulb dissipates 60 W of power.

The voltage applied to the light bulb is 120 V (in the US)

0.50 A

Note: most breakers in a home are set to trip at 15 A. So, one circuit in a breaker box can power 30 60 W light bulbs, or 1800 W.

(Old) Light Bulb Examples

Which has a larger resistance, a 100 W light bulb, or a 60 W light bulb?

(Old) Light Bulb Examples

Which has a longer filament, a 100 W light bulb, or a 60 W light bulb (assuming the diameters are the same)?

Extension Cord Example

“Perfect” Wires

• If we connect resistors in series, their resistances add together
• Real wires have resistance, which means that the resistance connected to an emf will be increased by using wires.
• If this resistance is significant, then we explicitly draw them in our circuit diagram.

Extension Cord Example

• If you use an extension cord with non-zero resistance to plug in some appliance, the power available to the appliance will be less than if you just plug it into the wall.

If an appliance uses 1000 W of power when connected to a wall outlet, how much power will it consume if it is connected to the wall using an extension cord with a 3 \(\Omega\) resistance in each wire?

Internal Resistance

• Real batteries have an internal resistance.

• This limits the maximum amount of current we can get out of them.

Internal Resistance

What is the internal resistance of our battery?

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The hydraulic (water) analogy

An analogy between the flow of water and electrical current can be made.

Dissipated Power

• Consider the energy that a charge \(dq\) loses as it passes through a resistor.
• This power is either turned into heat, work, or both.
• Charge is conserved. Only energy is transferred.
• Does the charge lose kinetic energy or potential energy?

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