AC Circuit: Finding I(t) general question

[charlies1902]

When you're asked to find I(t) in an AC circuit, what form does I(t) need to be in?
I remember from a long time ago that when the '(t)' is included you have to have it in a specific form.

 

[Simon Bridge]

The correct form is the one which gives a predictions consistent with measurements.

Usually, when the "(t)" (means "function of time") is included, the current is called i(t) and not I(t). Caps are reserved for constants as in $i(t)=I\cos(\omega t)$.

The exact form that the function i(t) has will depend on the circuit and the driving function ... which, in context, would be given as v(t). The function i(t) will be the solution to the differential equation modelling the system.

For sinusoidal driving functions, you'd have solutions in the form of complex exponentials which may be convenient to write down as trig functions. Impulses, though, produce transients - and, with feedback, the functions can be quite complicated.

 

[charlies1902]

The correct form is the one which gives a predictions consistent with measurements.

Usually, when the "(t)" (means "function of time") is included, the current is called i(t) and not I(t). Caps are reserved for constants as in $i(t)=I\cos(\omega t)$.

The exact form that the function i(t) has will depend on the circuit and the driving function ... which, in context, would be given as v(t). The function i(t) will be the solution to the differential equation modelling the system.

For sinusoidal driving functions, you'd have solutions in the form of complex exponentials which may be convenient to write down as trig functions. Impulses, though, produce transients - and, with feedback, the functions can be quite complicated.

Thank you.

In the book I'm using, they used capital I(t).

 

[Simon Bridge]

Yeh well - it's not compulsory.
Technically you can use any letters you like, as long as you are consistent (or signal your inconsistencies).

The first sentence is the bottom line though.
With the caveats that (a) other people have to be able to understand it, and (b) the examiner has to recognize it as the correct answer for you to get the marks in an exam.
You didn't realize it was this wide open did you? ;)

 

[Nickie]

In an AC circuit, the current is constantly changing direction and magnitude. Therefore, in order to accurately represent the current at any given time, I(t) must be expressed in a time-dependent form. This can be achieved by using either a sinusoidal function, such as I(t) = I0sin(ωt), or a complex exponential function, such as I(t) = I0e^(jωt). Both of these forms allow for the representation of the changing current over time in an AC circuit. It is important to note that the choice of form may depend on the specific circuit and its components, and it is always recommended to check with the circuit's equations and boundary conditions to ensure the correct form of I(t) is being used.