Question of the Week No.8 (Physics)
Consider the following schematic of a circuit that is set up in a series and parallel configuration:
A) Find the total resistance of the circuit.
B) Find the total current going through the circuit.
C) Find the current going through the 30 ohm resistor branch and use this to find the current going through the 7 ohm and 8 ohm resistor branch.
Explanation for A: Welcome back smart people to QOTW #8. This exercise is pretty simple, all you need to know to find the answers to parts A-C is a rudimentary understanding of how circuits work when its constructed in a series and parallel conformation.
Lets go ahead and consider part A where all that we’re interested in, is finding the total resistance of the circuit. Lets go ahead and label the branch that contains the 7 ohm and 8 ohm resistor as branch 1. Similarly, lets also label the branch that contains the 30 ohm resistor as branch 2.
Now, in branch 1 (B1), the two resistors are in a series conformation so to find the total resistance in branch 1 we just add them and combine them into a 15 ohm resistor. At this point, we haven’t done anything to modify branch 2 (B2) so we’ll just leave it there for now. Thus, our circuit is transformed into the following conformation:
Once we have this circuit in the aforementioned picture, we can realize that the resistor in branch 1 and the resistor in branch 2 are in a parallel configuration. To combine resistors that are in a parallel configuration we carry out the following operation:
Thus, when we combine the resistances in branches 1 and 2, we get that the combined resistance is 10 ohms. Therefore, our circuit can be updated and can be redrawn like this:
Thus, for part A, the total resistance of the circuit is 10 ohms.
Explanation for B: So, know that we’ve simplified our circuit as much as possible, all we want to do for part B is find the total current running through the circuit. In this case, we’ll just use the equation that describes current which is I = V/R where I represents current, V represents voltage, and R represents resistance.
Thus, the total current running through the circuit is 3 amps.
Explanation for C: Last part! All we’re concerned with in part C, is finding the current that runs through branch 1 and branch 2. Now, we know that the total current for the entire circuit is 3 amps. But, consider the following illustration:
When the current gets to point A, it splits, therefore it is no longer 3 amps since we have some current that is traveling through branch 1 and some current that is traveling through branch 2; but, as soon as it joins up at point B, 3 amps come out and travel around the circuit to repeat the process. So, how much current is flowing through branch 1 and how much current is flowing through branch 2?
To answer this question, you have to be familiar with a property inherent to parallel circuits. This property is that the voltage flowing through all branches is the same. Thus, the voltage flowing through branch 1 is 30 volts and the voltage flowing through branch 2 is also 30 volts. Thus, with this information we can find the current flowing through branch 2 and with some simple subtraction, we can find the current through branch 1.
Alright smart nerds, happy studying and see you in a bit :)
