Can Geometry Always Determine Voltage from Current Graphs in Circuit Analysis?

[theman408]

Homework Statement

In my Engineering Circuit Analysis I class I am in Capacitors and Inductors where they give us the graph of either i(t) or v(t) and we have to determine the graph of current or voltage depending if it's a capacitor or inductor.

Homework Equations

For example,
v(t)= L di/dt is the differential equation used and if you integrate it you get the current equation for the inductor.

The Attempt at a Solution

My question is, if you have a graph say current for a capacitor and ur asked to determine the graph of voltage for it, When cannot i not use the Geometry to determine the integration? When is that i have to use the slope-point equation to determine the line equation.?

My professor told me that i can use 1/2 base height or base height if it was geometrically possible to agilize the problem but sometimes it wasn't that straight forward, therefore i have to determine the equation so i can integrate it.

 

[Redbelly98]

You can use geometry to get the integral when the graph happens to be a simple geometric figure, such as a triangle or rectangle.

If the graph is more complex in form, you would need to deal with the equation for the graph in order to get the integral.

 

[Mene]

I would like to clarify that voltage and current graphs are important tools in understanding the behavior of electrical circuits. In this case, it is important to understand the relationship between current and voltage for capacitors and inductors.

When given a graph of current for a capacitor, the voltage can be determined by using the equation v(t) = 1/C ∫i(t)dt, where C is the capacitance. This equation is derived from the differential equation v(t) = C dV/dt, which relates the voltage and current for a capacitor.

However, for more complex circuits, it may not be possible to determine the voltage graph using geometry alone. In these cases, it is necessary to use the slope-point equation to determine the line equation and then integrate it to get the voltage graph.

It is important to understand the underlying principles and equations governing the behavior of circuits, as well as the limitations of using geometry to determine graphs. it is important to approach problems with a thorough understanding of the concepts and equations involved.