5/26/15 - Inductance Cont.

Today, we start off by drawing the curve of current in a R-L circuit. We draw it as an exponential growth curve.

After all the demonstrations, we're given a resistor and induct or to use in our data collection. 

Here is the measurement of the resistor from reading the colour stripes on the resistor.

Given the formula we derived last week for inductance, we calculate our theoretical value for inductance. We also calculate the resistance of the inductance coil since it is made out of copper wire.

Since we have the period from the time constant, we can calculate the frequency of the wave. 

Here we hook up a function generator to the oscilloscope. As shown, we can see the square wave on the oscilloscope.

Here we hook up the resistor in series with the inductor...which was wrong. It produced an interest graph though.

Here we did the calculations for the induction coil we used in the actual circuit.

We found a new resistance and a new time constant.

This time constant is also calculated with the resistance of the resistor in the circuit and the approximate resistance of the function generator.

Given the new time constant, we found a new frequency.

With the correct circuit, we can see the graph on the oscilloscope is showing the exponential inclines and declines.

Zooming in, we can see the curve more clearly, however it is still hard to measure since it is still an analog graph.

When we zoom in and scale the graph, we attempt to make a measurement for the period of the wave.

Using the half time constant formula, we calculate an approximate time constant.

We multiply the time constant by the resistance and find an approximate inductance for our circuit. We then solve for the amount of loops in the inductor and find a value with a large error.

We estimate this error is due to the analog graph and uncertainty of the resistance in the function generator.

Given an Active Physics web app again, we answer some questions on the demonstration. We realize that we've already done the same one before and move on. Thankfully we move on, since our app crashed.

The last thing we observe in class is a R-L circuit.

We observe the top and middle branches' inductance time constants.

Since we can find the max currents, we can find the current through the circuit at any given time.

The middle branch only has an inductor, so that branch is instantly at max current.

The top branch we find the current based on the max current at a time after the switch is closed.

We notice that the voltage across the middle resistor is, as expected, 45V; but the top branch has a potential difference drop across the resistor that is lower than the max due to the inductor.

Now given a potential difference, we're asked to find the time it takes to reach that potential difference.

 Since the voltage of the resistor is the max voltage minus the inductor's voltage, we find that potential difference across the resistor. Since we have the current current flowing through the branch, we can back substitute into the formula and solve for the time.

Finally, we solve for the energy stored in the inductor with the formula of half inductance times current squared.  We notice it has a very small amount of energy stored.