Does the R vs. tau Graph in RC Circuits Always Pass Through the Origin?

[julesshmules]

Homework Statement

In an RC circuit, should a graph of R vs. tau necessarily go through the origin? What does a non-zero intercept indicate?

Homework Equations

The Attempt at a Solution

My graphs look like they go through the origin, and from the equation tau = RC, I would expect that when R is zero, tau is also necessarily zero. However, from the definition of tau as the time necessary for the charge on a capacitor to go from 0 to 63.2% of the max charge, it seems to me that tau can never actually be zero. Also, because the wires themselves have some degree of resistance, R seems like it would never actually be zero either. I'm not sure which idea to go with.


Thanks for your help!

 

[anathema]

I can tell you that a graph of R vs. tau does not necessarily have to go through the origin. This is because the value of tau is not solely determined by the value of R, but also by the capacitance (C) in the circuit. The equation tau = RC assumes that C is a constant, but in reality, it can vary depending on the type of capacitor used.

A non-zero intercept on the R vs. tau graph indicates that there is another factor affecting the value of tau, such as the capacitance. It could also indicate measurement errors or other external factors that may affect the circuit.

In order to accurately determine the relationship between R and tau, it is important to keep all other variables constant and to use a variety of values for R and C in the circuit. This will help to create a more accurate graph and determine the true nature of the relationship between R and tau.

I hope this helps to clarify any confusion and guide your further experimentation. Remember, as scientists, we must always consider all factors and variables in order to draw accurate conclusions.

 

[ogb p]

I would like to clarify that the graph of R vs. tau does not necessarily have to go through the origin. The equation tau = RC assumes ideal conditions, where R is zero and the capacitor can charge instantaneously. However, in real-life circuits, there will always be some resistance and it takes some time for the capacitor to charge. Therefore, a non-zero intercept on the graph indicates the presence of resistance and the time it takes for the capacitor to charge. In fact, the value of the intercept can provide useful information about the resistance and the time constant of the circuit. So, it is important to consider the non-zero intercept and not assume that the graph will always go through the origin.