There are three different kinds of electric circuit connections: series, parallel, and series-parallel (complex) connections. The specific kind of circuit we used is called a DC (Direct Current) circuit. A DC circuit calls for a closed circuit of constant voltages, currents, and resistors and is energized by a generator, such as a battery. Using an online PhET Circuit Construction Kit, I constructed a virtual example of each type of connection. An important equation to remember throughout this presentation is that voltage is equal to the product of current and resistance (V = IR).
I first built a series connection using two light bulbs and a single battery for energy. A series connection is when resistors are connected along a single wire path so that all of the electrons from the battery flow continuously through that one path. The total current (flow of charge) is the same as the current in both the first and second light bulbs, because there is only one path for the current to travel along and therefore the current is never divided or changed due to separate pathways. The total voltage drop in a series circuit is equal to the sum of the voltage drops in the first and second light bulbs. The resistance in a series connection increases as you add more resistors, because with each resistor comes more resistance along the wire path. If either one of the bulbs was removed, the remaining bulb would not be lit. This would happen because by removing a bulb, the circuit would no longer be closed and the path would have a gap where the bulb once was. The current would have no way of reaching the remaining bulb.
The second connection I built was a parallel connection using the same elements as before: two light bulbs and a battery. A parallel connection is when each resistor in the circuit is connected on its own new path. The total current is equal to the sum of the currents in each resistor. Instead of having only one path for the current to travel along, there are three separate paths. The current splits between these three paths, which is why the sum of the current in each of these paths would add up to the total current. The total voltage drop is equivalent to the voltage drop in each resistor. This is because the voltage travels into each path at a voltage equivalent to the original voltage of the battery and there is an equal voltage drop in each resistor. The resistance in a parallel connection decreases as you add more resistors. If either of the bulbs was removed, the remaining bulb would remain lit and shine even brighter than originally. The circuit would still be closed, because removing one of the light bulbs only cuts off one of the two paths that the current could travel on. The current no longer divides itself because there is only one path available for travel, and therefore the remaining bulb shines brighter due to the increased current.
The final connection I built was a complex connection using the same single battery for power as before. My complex connection consisted of a series connection between a single light bulb and a parallel connection of two more light-bulbs. In order to solve for the total current for a complex connection such as this one, the total equivalent resistance of the entire circuit must be found first by adding the equivalent resistance of the parallel circuit to the equivalent resistance of the series circuit. Here is why we use this equation: as I stated earlier, this is a complex version of a series connection, which requires us to add the resistance of each light bulb along the path of the wire. The parallel connection is viewed as a single light bulb along said path, reasoned for by Kirchhoff's first law about the conservation of charge. His law states that the sum of the currents entering a junction (such as this parallel connection) is equal to the sum of the currents leaving that junction. In other words, the current travels through the parallel connection in the same unchanging way as in a light bulb - the only difference is that it splits itself between a group of new paths and then regroups at the end of the junction. Once the total equivalent resistance of the entire circuit has been found, it can be used to solve for the total current. Since this complex connection is just a complicated version of a series connection, the total voltage drop is equal to the sum of the voltage drops on the circuit. First, the voltage drop of the series resistor is solved for by multiplying the total current of the circuit by the lightbulb's resistance. We can derive from the total voltage drop equation that the voltage drop in the parallel connection is equal to the difference between the total voltage of the circuit and the voltage drop in the series resistor. From there, we can also figure out that the voltage drop in the parallel connection is equal to the voltage drop in each lightbulb in said connection. If the light bulb in series was unscrewed from the circuit, the remaining light bulbs from the parallel connection would immediately go out. This is because, as I mentioned before, the current would have no way of reaching the parallel connection if the light bulb it was in series with was unscrewed and the path was cut off. If either the light bulb at the bottom or at the top of the parallel connection was to be unscrewed, the remaining bulb in the parallel connection would form a normal series connection with the series bulb. This would happen because by removing one of the two parallel bulbs, we are breaking off one path and leaving the current only one possible path to travel on.
The second connection I built was a parallel connection using the same elements as before: two light bulbs and a battery. A parallel connection is when each resistor in the circuit is connected on its own new path. The total current is equal to the sum of the currents in each resistor. Instead of having only one path for the current to travel along, there are three separate paths. The current splits between these three paths, which is why the sum of the current in each of these paths would add up to the total current. The total voltage drop is equivalent to the voltage drop in each resistor. This is because the voltage travels into each path at a voltage equivalent to the original voltage of the battery and there is an equal voltage drop in each resistor. The resistance in a parallel connection decreases as you add more resistors. If either of the bulbs was removed, the remaining bulb would remain lit and shine even brighter than originally. The circuit would still be closed, because removing one of the light bulbs only cuts off one of the two paths that the current could travel on. The current no longer divides itself because there is only one path available for travel, and therefore the remaining bulb shines brighter due to the increased current.
The final connection I built was a complex connection using the same single battery for power as before. My complex connection consisted of a series connection between a single light bulb and a parallel connection of two more light-bulbs. In order to solve for the total current for a complex connection such as this one, the total equivalent resistance of the entire circuit must be found first by adding the equivalent resistance of the parallel circuit to the equivalent resistance of the series circuit. Here is why we use this equation: as I stated earlier, this is a complex version of a series connection, which requires us to add the resistance of each light bulb along the path of the wire. The parallel connection is viewed as a single light bulb along said path, reasoned for by Kirchhoff's first law about the conservation of charge. His law states that the sum of the currents entering a junction (such as this parallel connection) is equal to the sum of the currents leaving that junction. In other words, the current travels through the parallel connection in the same unchanging way as in a light bulb - the only difference is that it splits itself between a group of new paths and then regroups at the end of the junction. Once the total equivalent resistance of the entire circuit has been found, it can be used to solve for the total current. Since this complex connection is just a complicated version of a series connection, the total voltage drop is equal to the sum of the voltage drops on the circuit. First, the voltage drop of the series resistor is solved for by multiplying the total current of the circuit by the lightbulb's resistance. We can derive from the total voltage drop equation that the voltage drop in the parallel connection is equal to the difference between the total voltage of the circuit and the voltage drop in the series resistor. From there, we can also figure out that the voltage drop in the parallel connection is equal to the voltage drop in each lightbulb in said connection. If the light bulb in series was unscrewed from the circuit, the remaining light bulbs from the parallel connection would immediately go out. This is because, as I mentioned before, the current would have no way of reaching the parallel connection if the light bulb it was in series with was unscrewed and the path was cut off. If either the light bulb at the bottom or at the top of the parallel connection was to be unscrewed, the remaining bulb in the parallel connection would form a normal series connection with the series bulb. This would happen because by removing one of the two parallel bulbs, we are breaking off one path and leaving the current only one possible path to travel on.
