3/1/16 Day 3: Series and Parallel Resistors and Voltage Division

Today we did a teaser problem involving running a 120 V electric potential between the ends of a hot dog and predicting what would happen. Then LEDs were placed parallel and perpendicular to the hot dog and the prediction of whether they would light on or not and the brightness of each was predicted. Next, we used Kirchhoff's Laws for an example problem to find voltage and current of a component in a circuit containing a dependent source. We then learned about series and parallel resistors and finding equivalent resistance and conductance, followed by dividing voltage in a circuit. Lastly, the "Dusk-to-Dawn Light" lab was performed, where a nightlight was invented.


LECTURE:

Above is a picture of the teaser hot dog problem. First no LEDs were in the hot dog (in contrast to the picture above), and a 120 V potential difference was placed across it. As seen below, it was predicted that the hot dog would cook slowly, and that the current would be highest at first then drop down due to the evaporation of water and reduction of ionic salts.

The prediction was then put to a test.

As seen in the video above, our prediction was correct! The hot dog did start to cook slowly, albeit in a more dangerous and less tasty manner than on a grill.

The LED's were then added to the hot dog in a perpendicular and parallel fashion, with some of the parallel LED's having their legs moved further apart.

It was predicted that all of the LEDs would light, with our hypothesis stemming from the fact that a hot dog contains a lot of resistance so the current would not be unidirectional. 

However, our hypothesis was wrong! Only the parallel LEDs did light up, with the ones whose legs stretched our further being the brightest. The current is in fact unidirectional, so the LEDs in parallel had a voltage difference whereas the ones perpendicular weren't. Also, with legs further apart there was a higher voltage difference, causing a greater current and a brighter light emitted.

Problems involving finding the current through and voltage of a component in a dependent source circuit were then solved, and are shown below:

Kirchhoff's Voltage and Current Laws were used to solve the above problems.

In this problem, a simple circuit involving a voltage source and two resistors was provided, and the problem asked to find the voltage going out of the circuit as a function of the resistors and voltage going in. It was found that V out is just equal to voltage across the second resistor.

Then values were given for V in (12 V), current (10 mA) and V out (3.3 V) and the resistances of each resistor were obtained.

The problem was taken even further and engineering concepts were added to it. These include cost and using resources possible to obtain. No resistor has a resistance value of 870 ohms, and it would be too expensive to create one. Therefore new resistors with resistance values found in cheap ones had to be chosen, and they needed to work with our circuit. A 1500 ohm and 560 ohm resistor was decided to be used, which lowered the current to 5.8 mA and slightly lowered V out to 3.26 V, which is close enough for our purposes.

In this problem, which is very similar to the last one, an LED was replaced with a resistor. The LED had a functioning voltage of 3 to 3.6 V, and a working current of 100 to 120 mA. Using those restrictions by the LED, an appropriate resistor had to be chosen, and the power had to be determined for that resistor. The appropriate ressitor could have a range of 5 to 12 ohms, and the power based on that range can be anywhere from 0.06 W to 0.144 W.

In this problem, the equivalent resistance of this circuit was obtained, and it was found to be just R.

LAB (Dusk-to-Dawn Light):

Purpose:

The purpose of this experiment was to create a night light (i.e. a light that automatically turns on when the ambient light level gets too low) out of a diode, a bipolar junction transistor (BJT) and a photocell. A photocell is an alternating resistor that is dependent on the amount of ambient light; the lower the light level, the higher the resistance of the photocell becomes. 

Pre-lab:

In the above picture is the pre-lab of this experiment. The goal was to find the voltages across the photocell if it had a resistance of 5,000 ohms for one situation and 20,000 ohms for the other situation. The voltage for a 5,000 ohm resistance was calculated to be 1.67 V, and 3.33 V for a 20,000 ohm resistance.

Apparatus:

The equipment for this experiment included an analog discovery tool connected to a computer containing "Waveforms" software, which was used to supply a constant 5 V to the circuit. A breadboard was also used to make the circuit on, and wires were used to connect the components of the circuit together. A photocell and a BJT were also used in this experiment to control the current through the system; a BJT is a current-controlled current source. Lastly, a 10,000 ohm resistor, a diode and a digital multimeter were used. The diode was used to confirm the working of the photocell and to produce the green night light. The digital multimeter was used both as an ohmmeter and a voltmeter, to measure resistance and voltage, respectively.

Procedure:

The circuit shown in the schematics above was created on a breadboard. The 5V power supply was connected in parallel to both the 10 kohm resistor and the collector of the BJT. The 10k ohm resistor was then attached to the base of the BJT, along with the photocell. The LED was then attached to the emitter of the BJT, and the photocell and LED connected back together to the 5V power supply. This setup of the circuit is seen below:

In this circuit, when the ambient light level is high, the photocell has a lower resistance, allowing current to run through it and basically preventing almost all current from entering the base of the BJT. Not allowing current through the base results in the emitter and collector being disconnected in the BJT, and therefore not allowing current to run through the diode. This results in the current not lighting up. When the ambient light level is low, the resistance increases exponentially in the photocell, and this results in the funneling of all current to the base of the BJT. Doing so links the collector and emitter of the BJT, resulting in current flow through the diode and light being emitted from it. This process is seen in the cool and short video below:

Data:

The picture above contains the resistance of the photocell in light and dark situations, as well as the base voltage of the BJT and the voltage across the diode in light and dark conditions. The voltages were measured by attaching the voltmeter parallel to the photocell and diode. 

Conclusion:

As expected, the voltage across the diode is negligible in light conditions and much higher in dark conditions. The voltage difference in dark conditions causes it to light up, and is all controlled by the photocell and the BJT, as explained above in the procedure. In addition, the voltage difference across the BJT is higher in dark conditions, which is expected because current in the base of the BJT leads to the connection between the emitter and collector and therefore current. 

Unfortunately, due to the resistances of the photocell being completely different than the theoretical resistances, it was not possible to compare the measured values of voltage to the actual voltage. It is not known why the resistance of the photocell was changed so dramatically with the change in light level.