The concept of time has been a constant question for humans since the beginning of time. Well, maybe not that literal, but it has been a constant question throughout history as well as in modern day.
Questions like: How do we know time exists? What is time? and How does time work? have all been asked by average people and famous scientists alike.
As noted by Dr. Albert Einstein, the father of Relativity, “time is something that happens to us”. He also stated that “time is an illusion”, making it clear that he did not believe that there was such a thing as absolute time.
There are three dimensions in the universe: length, width, and depth. Length and width are both related to spatial dimensions, or how things exist in space. Depth is related to temporal dimensions, or how things exist in time.
Initial conditions
The initial condition of the figure skating world was that the compulsory dances were dominant. The ice dance revolution changed this, creating a separate category for artistic performances.
Compulsory dances were sequences of moves that all skaters had to perform. They were designed to test basic skills like turning and shifting levels.
The introduction of the short program also helped shift the dominance of figure skating towards artistry. By having a shorter, more focused program, skaters could showcase more complex elements and routines.
The last significant change in the figure skating world was the removal of grades of execution (GOE) for jumps. This meant that judges could not give higher or lower scores for jumps based on technical perfection.
Determining current at t = 0 s
The initial current at time t = 0 s can be determined by examining the circuit for a short period of time prior to t = 0 s.
For example, if the switch has been open for a long time and the circuit is examined just before t = 0 s, then the current can be determined by examining the length of time the switch has been open and how much charge has passed through the circuit.
Since no charge passes through the circuit at t = 0 s, then no current will be observed at that instant. The current at any other instant prior to t = 0 s can be determined by examining how much charge passes through the circuit at that instant.
The current at any point in time after t = 0 s can be determined in a similar manner as before: by observing how much charge passes through the circuit at that instant.
Calculating current at t = 0 s
Now, let’s look at what happens when the switch is open at t = 0 s, when the current flows into the circuit.
We know that the current entering the circuit is I0, but we need to find out how much current is flowing through each part of the circuit. We can do this by looking at what region of the circuit has what voltage across it.
The upper portion of the circle has a voltage of Vin − Vout, or 12 − 0, so there is a 12 V difference across that part of the circle. We can write this as 12 I(circle) 0 = ΣI(circle)=I0Σ=0. This just means that there is zero current flowing through that part of the circle.
Determining voltage at t = 0 s
Now, let’s talk about how to determine the voltage at time t = 0 s. This is an important question to answer, because it determines what state the circuit is in when the switch is closed.
If there is no current flowing in the circuit at time t = 0 s, then the voltage across the terminals of the battery must be equal to the voltage across the terminals of the capacitor. These are independent components, so their voltages must be equal.
Since we have proven that there is no current flowing in the circuit at t = 0 s, then there must be no current flowing at any other time either. The only difference between times is whether or not the switch is open or closed. Therefore, if there is no current flowing in the circuit at time t = 0 s, then there will not be any current flowing at any other time either.
Calculating voltage at t = 0 s
Now let’s look at what happens when the voltage is already established, as in this problem.
The current is already flowing, so we can’t use I to represent the current. Instead, we’ll use A for amperes, the SI unit for electric current.
Since there is a certain amount of time that has passed (T) from t = 0 s until now, we can use T and t = 0 s interchangeably. The only difference is that t = 0 s refers to the very beginning of time (or the start of this problem), and T refers to the length of time from then until now.
We are given the initial potential difference V0, which we will substitute for |V|. We are also given the length of time that the switch has been open t
We know that I=AΔt, so we can substitute A and Δt for I in our final answer.
We also know that V=IR, so we can substitute R for IR in our final answer.
