# 9.2: Activities

- Page ID
- 28147

## Things You Will Need

Nothing! All the data has been meticulously collected for you.

## The Data

We start with the basic values we measured with the ohmmeter and voltmeter.

**emf of the battery**– This is the terminal voltage of the battery when no current is flowing, measured by a voltmeter (which has essentially infinite resistance).

**resistance of the resistor**– Make a special note of the units of this measurement.

**resistance of the inductor**– Make a special note of the units of this measurement.

**voltmeter reading vs time**– This is a graph of the time-dependent voltage drop across the leads of the voltmeter shown in the diagram found in the Background Material. The value of the voltage during the "before" period of time is highlighted in the red box.

**voltage readings during the "after" period**– The table below contains individual data points taken from the graph above, each separated by an equal time interval of 0.0001 seconds.

## Internal Resistance of the Battery

There is a discrepancy in two measurements of voltage across the leads of the battery: The multimeter connected directly to the battery gives a higher reading for the voltage difference across the terminals than the voltmeter gives which the battery is in the circuit with the switch closed.

- Use the difference in these readings and other data given above to find the internal resistance of the battery. [
*Note: The value you will get will be significantly higher than what what you might find online as a typical internal resistance for a D-cell battery battery. This is probably mostly due to the fact that the battery used was quite worn-down (near the end of its life cycle), and internal resistance increases substantially in batteries as they age. There is also a significant amount of uncertainty in the**calibrations of the multimeter and the voltmeter that produced the graph.*]

## Action of the Inductor

Ignoring the squiggles in the graph that occur around the time \(0.4810s\), there is a rather sudden jump (and a sign change!) in the voltage across the voltmeter (which is connected across the inductor) when the switch is suddenly opened. [*Note: The squiggles in the graph are unavoidable because it is impossible to open the switch fast enough when a data point is collected every 0.00002 seconds. For example, when the gap in the switch is still very tiny, it behaves briefly like a capacitor.*]

- Consider the sudden jump in the graph when the switch is opened.
- Explain the physics of what is happening here. Make a note of what currents are flowing right before the switch is opened, and what effect the inductor will have immediately after it is opened.
- Why does the sign of the voltage difference change?
- Compute what you would expect the peak voltage of that jump to be, and compare it with the peak in the graph. Can you think of a reason why these values do not match? [
*Hint: Voltage measurements are taken every 0.00002 seconds, but what are the odds that the peak of the graph occurs exactly when a voltage measurement is taken?*]

Our next task is to use a graph of the decay data to determine the inductance of the inductor. As a reminder, the time-dependence of the current in a decaying LR circuit is given by:

\[I(t) = I_oe^{-\frac{t}{\tau}},\;\;\;\;\;\tau\equiv\dfrac{L}{R}\]

- Obtain the time constant of the circuit.
- Fill-in the third column of the table with appropriate calculated values which result in a graph vs. time that we expect to be a straight line.
- Make a plot of your computed third column numbers vs. time, and insert a best-fit line.
- Use the best-fit line to extract the time constant of the circuit.

- Compute the inductance of the inductor from the time constant and other data available.

## Lab Report

Download, print, and complete this document, then upload your lab report to Canvas. [*If you don't have a printer, then two other options are to edit the pdf directly on a computer, or create a facsimile of the lab report format by hand.*]