Modeling emf, Potential Difference, and Internal Resistance

The goal of this activity is to help students develop an accurate model for internal resistance.

Specifically, students should be able to distinguish emf from electric potential difference for an open and closed circuit after comparing models of various electric circuits.
Student use of a Java based circuit simulator may be required for supplemental assignments.

• Educational level: AP Physics / College / University
• Setting: Class lecture supplement, source of peer interaction questions
• Time required: 40 - 50 minutes
• Special equipment: Access to internet, digital projector; voltmeter, battery, wires, and light (or other element) for creating a demonstration circuit
• Pre-requisite knowledge: Ohm's law

SETUP AND INTRODUCTION

To prepare for use in the class, the instructor should have

• A Java capable computer connected to the internet.
• The computer needs to be connected to a digital projector for use in class.
• Browse to Circuit Construction Kit III to open the applet.
• Although running Circuit Construction Kit III is intuitive (dragging and dropping circuit elements into place), files can be created ahead of time within the applet for opening at a later time for speedy set up.

 Example Guiding Questions:

• "Does a '9V' battery always provide 9 volts?"
  Demonstrate with a real battery that the potential difference indicated by the voltmeter is not exactly what's printed on the battery.
• "Is this the same potential difference a battery supplies for an element in a complete circuit?"
  If possible, complete a circuit with the battery and show that the potential difference is not the same as it was before.
• Why might manufacturers produce batteries with potential differences greater than what's advertised?"
• "Are wires free of electrical resistance (under normal conditions! i.e. room temperature.)?"

Setting the Stage: The difference between ε and ΔV

Create (or load) a circuit that has a battery, a resistor (0 Ω), a switch, and another resistor (10 Ω) in series to display to the class on screen. With the switch open, ask students to work in pairs to predict which segments of the circuit would have the greatest and the least "voltage" readings.

Instead of immediately polling students for their answers, ask the same question after closing the circuit switch. Again, allow a couple of minutes for students to work with one another and arrive at their answers.

Correct answers for the circuit with the open switch are that only segments including the battery and not the switch will produce a reading on the voltmeter. This value should be the same as the labeled power source (ε). For the case of the closed circuit, the greatest potential drops are across elements of greatest resistance.

To facilitate class participation, lead a class discussion eliciting students' ideas about whether there should or shouldn't be a difference if the switch is closed. Some example questions to assist discussion include:

• Does a stand-a-lone battery have current?
• What's the first requirement of a complete circuit?
• How would you define a perfect wire?
• How would you define a perfect batter?

The close of this section should be precipitated by asking students to describe the conditions necessary for the voltmeter readings to be less than the value indicated on the battery.

Internal Resistance: Effectively a small resistor inside the battery

With the leads of the voltmeter across one end of the battery and the opposite end of the 0 Ω resistor, the potential difference should be very nearly 9.0V (slightly less due to wire resistance). 

1. Remove one of the voltmeter leads from the closed circuit.
2. Right click on the resistor and select "Change Resistance" (the pop-up box should be moved so that it is not overlapping the voltmeter).
3. Increase the resistance of the resistor to 50 Ω.
4. Reconnect the loose voltmeter lead to the circuit.

Ask the students the following questions:

• If the resistance of the resistor is decreased or increased, will the reading on the voltmeter change? If so, how? (as r decreases, ΔV approaches ε)
• How would your answers change if the circuit were open? (no change, ε)

As the resistance of the resistor is changed by sliding the bar, the voltmeter's value changes real-time, so demonstrating the relationship is easy once students have discussed the question in pairs.

Now remove the resistor near the battery and replace the void with a wire to complete the circuit. Right click on the battery to reveal how its internal resistance can be changed. Stress that the only difference now is that the probes of a voltmeter can't be 'snuck' in, avoiding the internal resistance as done up to now. Such is the case with real batteries.

To simplify the general appearance of the circuit and eliminate possible distractions: After loading the applet, it may be helpful to select "schematic" and the "show values" checkbox. Also, press "Enable >>" in the Advanced frame to select the "Hide Electrons" check box.

In the Tools frame, check the "Voltmeter" check box to bring the voltmeter into view. The voltmeter and its leads can be dragged and dropped out of the way of the circuit if need be.

To display values of potential differences and resistances on screen, right click on the circuit element to bring up a drop down box and select the desired action.

Reflecting back to this content while studying AC circuits may help students put in context why it is household electricity is via AC and not DC electricity.

Throughout the activity, student participation and evolving class discussions serve as informal assessment. Following class, students could be provided with related assignment problems or instructed to use the applet themselves for a grade: Sample Assessment (Microsoft Word 21kB Jul22 07).

The applet used in this activity is managed by PhET (Physics Education Technology)
Circuit Construction Kit