Physics 2212, Lab 12: Inductance and RL Circuits

Eric Murray, Fall 2006

Question these experiments will enable you to answer: Is the inductance of your inductor within the manufacturer's tolerance? What is the time constant of your RL circuit?

Features: First, the circuit element investigated is an inductor. Devices that are interfaced to a computer are used to apply a sinusoidal potential difference and measure the resulting current. Inductive reactance is calculated as the slope of a peak potential vs. peak current plot. Inductance is calculated from inductive reactance and frequency.

Next, a series RL circuit is investigated. As a potential difference is applied or removed across the circuit, the potential difference across the inductor, the potential difference across the resistor, and the current through the circuit, decay exponentially with time. Fitting a general exponential decay curve to the appropriate portions of the graphs enables the time constant of the circuit to be calculated.

Preliminaries: Build the 8.2 mH inductor circuit. The potential difference is supplied by the "output" sockets, and measured by a voltage sensor in analog channel A. (The supplied current will be measured by the PASCO interface internally.) There are many valid ways to build this circuit, but an example is illustrated (and linked to a larger image). Open the data template. You'll find a graph for the potential across the inductor and the current provided by the PASCO interface function generator as a function of time. The function generator is set to provide a potential difference that varies sinusoidally with time at 1000 Hz and having a 0.10 V amplitude. After Record is clicked, data will be collected at 40 kHz for 0.010 s. Nothing need be calibrated.

Experiment 1: Click Record. Data will be collected for 0.010 s. Fit sine curves to both the potential and current data. Note that the amplitude of the potential across the inductor may be less than the amplitude of the potential applied by the PASCO interface. Record the amplitudes of the potential across the inductor, and the current through it.

Repeat, increasing the applied potential amplitude in 0.10 V increments, ending with a 1.00 V data set. Record the amplitudes of the potential across the inductor, and the current through it. If you delete each data set before recording the next, the sine fit will automatically be made to the new data set.

Graph the amplitude of the potential across your inductor as a function of the current through it. Find the inductive reactance (slope of the graph) with its standard error. An Excel spreadsheet is recommended. Calculate the inductance and its standard error from the reactance results. The manufacturer of this inductor claims a tolerance of ±15%.

Experiment 2: Build a series RL circuit using your (nominally) 8.2 mH inductor and a 10 Ω resistor. You may measure the resistance of your resistor using your DMM. There are many valid ways to build this circuit, but an example is illustrated (and linked to a larger image). Predict the time constant for your circuit, and record your prediction.

The potential difference across the resistor is measured by a voltage sensor in analog channel A. The potential difference across the induct is measured by a voltage sensor in analog channel B. The supplied current will be measured by the PASCO interface internally. Open the data template. You'll find a graph for the potentials across the resistor and capacitor, and the current provided by the PASCO interface function generator, as a function of time. The function generator is set to provide a potential difference that varies with time as a 100 Hz positive square wave having a 4.0 V amplitude. Data will be collected for 0.010 s after Start is clicked, thereby capturing about one full cycle. Nothing need be calibrated.

Click Start. Once data collection is complete, select the region on the current vs. time graph that shows a complete decay half-cycle (i.e., current is positive and decreasing). Select a Natural Exponent Fit from the fit menu. Record the fit parameter B and its uncertainty ΔB. Calculate the time constant and its uncertainty.

Fit a Natural Exponent curve to the appropriate region of the resistor potential vs. time graph (potential positive and decreasing). Fit an Inverse Exponent curve to the appropriate region of the inductor potential vs. time graph (potential negative and increasing). Find the time constant and the uncertainty of each, as you did with the current. How do the three time constants compare to the value you predicted?

Summary: Review your worksheet. Think about the goals of these experiments, your results, and the expectations from theory while writing your discussion.