Circuit Theory
We have a circuit with two batteries in series, two lit bulbs on the opposite end, and in the middle is an open switch with an off bulb next to it. We were asked to predict what will happen to the bulbs once the switch is closed. We predicted that the upper and lower bulbs will remain the same, and that the center bulb will stay off.
As seen in the photo above, our prediction was correct! The lit bulbs stayed on with the same amount of light, and the bulb in the middle remained off. The reason for this is because each battery produces 1.5 V, and as the charge travels upward starting from the bottom battery, the charge builds up to 3V. As the charge travels across the circuit and reaches the top bulb on the right, it uses 1.5 V to light it. Afterwards, the rest of the charge travels through the bottom bulb to complete the circuit.
In the second circuit we needed to analyze, we have two 1.5 V batteries on the left lighting two bulbs in the center, and an open switch keeping a third battery from interaction with our circuit. We predicted that once the switch is closed, the upper bulb will be brighter, and the lower bulb will remain the same.
We ended up being incorrect in regards to this circuit. The upper bulb and lower bulb remained at the same level of brightness. The reason for this is because the power flowing through the 2 bulb/2 battery circuit remains the same. After closing the switch, the power flowing in from the third battery on the right stays continues to travel around the rectangular path on the right. One bulb takes 1.5 V, another 1.5 V is lost at the junction to the left of the switch, and the remaining 1.5 V goes into the lower bulb.
DC Circuit Analysis
For this activity, we used two bulbs and two batteries to make the bulbs as dim as possible, and as bright as possible. The table above are our results, which indicate that the bulbs dim when the bulbs themselves are in series, or if their batteries are parallel. Likewise, when the bulbs were parallel or the batteries were in series, it resulted in brighter bulbs.
We also needed to explain power in terms of voltage and current. Basically, the brightness on the bulb depends on the amount of power flowing through a circuit. Therefore, voltage and current affects the brightness of the bulbs.
Using a Multimeter
The first test we ran on how to use a multimeter involved creating a circuit like the one depicted above, and testing the amount of voltage flowing through the resistors. As you can see from the data above, the voltage of the battery power source doubled when we went from one to two batteries. The voltages at resistors 1 and 2 were equal when using 1 battery, and equal when using 2. What we realized is that the voltages in each resistor could be added up to get the value of the voltage in the power source.
Next, we created three more circuits as depicted above, and tested the voltages at various points (which are also shown in the diagrams) using 1 or 2 batteries as well. In the first circuit above (which is the same as the circuit from the first part of this activity), we realized that the current is equal throughout the entire circuit. The final two circuits shown above depict parallel resistors this time, instead of in series. What we realized in the final circuits are that the voltages flowing through the resistors are still equal, however the magnitude of voltages matches that of the power supply. Also, it turns out that the current decreases by half after passing through each resistor.
Voltage Law
The photos above summarize what was just learned, where in a parallel circuit, the voltage stays the same and the current divides: "Components connected in Parallel with each
other have the same voltage drop across. If one of the components is a
battery it is not a voltage drop but it is still the same voltage only now it
is a gain."
Alternatively, in a series circuit the voltage divides and the current stays the same: "Components connected in Series with each other
have the same current flowing through them (or the same charge if
they are capacitors)."
The theory behind why the circuits behave this way, is because it must obey the Voltage Law, which states that the next voltage in a circuit must be 0.
Resistor Color Code
We learned that resistors are color coded in a way that tells us their resistance in Ohms, as well as the amount of error in their values. Under the Theoretical table we have our interpretation of the codes of 4 different resistors, and under Actual we see the actual resistance of each piece after we manually tested them using a multimeter.
Below that data, we used three identical resistors of 620 Ohm +/- 5% (actual values are located at the very bottom of the photo above) and testing them in various circuits. What we saw is that when in series, the amount of resistance added up according to how many resistors were used. When in parallel, the amount of resistance divided by the amount of resistors used.
Now that we know and understand how resistors work in series and parallel, we were tasked with finding the total resistance of the system above. As you can see, we gradually combined the various R1 and R2 resistors in parallel and series until we ended up with a final resistance of 68 Ohms.
Kirchhoff's Laws
Depicted above is an example of Kirchhoff's Laws, which include the Loop Rule and Junction Rule. The Junction Rule states that the sum of all the currents entering any node or branch
point of a circuit must equal the sum
of all currents leaving the node. The Loop Rule states that around any closed loop in a circuit, the sum of all
emfs, voltage gains provided by batteries or other power sources, (e = emf) and all the potential drops across resistors
and other circuit elements must equal zero.
The way we implement this is to first assign currents to a circuit, and the apply the loop rule to (in this case) come up with three equations which we can use to solve for the current. We would have to solve for I2 and I3, then use the current rule to find I1, which equals I2+I3.
Summary:
In summary, we went over DC circuits and tested them in various layouts using a multimeter. We also anaylzed Voltage Law, and deciphered the color code on resistors. Finally, we went over Kirchhoff's Laws, which include the junction and loop rules. Using all we learned today, we are able to solve for various issues in circuits such as calculating the amount of current flowing through a circuit, and the total resistance that a circuit has, as well as what are the best circuit layouts for brightness and dimness.
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