Graphs of RC Circuit Responses

[stunner5000pt]

Homework Statement

What is the meaning of the area under an RC circuit's Current-Time & Voltage-Time graph while charging the Capacitor?

Relevant Equations

$$I = \frac{V}{R} \exp (\frac{-t}{RC} )$$

This isn't a homework question per se but I wanted to understand how integration can connect things.

If we integrated the area under the graph, would this give us the total charge to charge the capacitor?

My logic here is purely based on units - if we integrate current on a current-time graph, the units of the integral is Amp sec which is coulombs.

Another question is - what is the meaning of the area under the Voltage-Time graph represent? In this case, this would give us unit of magnetic flux (Volt sec) but is there any other meaning to this?

Thanks again for your help!

 

[DaveE]

Homework Statement: What is the meaning of the area under an RC circuit's Current-Time & Voltage-Time graph while charging the Capacitor?
Relevant Equations: $$I = \frac{V}{R} \exp (\frac{-t}{RC} )$$

This isn't a homework question per se but I wanted to understand how integration can connect things.

If we integrated the area under the graph, would this give us the total charge to charge the capacitor?

My logic here is purely based on units - if we integrate current on a current-time graph, the units of the integral is Amp sec which is coulombs.

Yes. This is basically the definition of current; the flow of charge. $Q=\int {i(t)} \, dt$, or $\frac{dQ(t)}{dt} = i(t)$

Another question is - what is the meaning of the area under the Voltage-Time graph represent? In this case, this would give us unit of magnetic flux (Volt sec) but is there any other meaning to this?

The relationship between current and voltage is in the definition of capacitance. Like this:
$CV(t) = Q(t) = \int_0^t {i(\tau)} \, d\tau + Q(0)$. So the voltage is essentially a scaled version of the capacitor charge.

You could certainly integrate the voltage (or charge) over time, but it's not clear to me what value that has. Maybe in more complex circuits? It would certainly be a valuable operation if you had an inductor across the capacitor, then you would know the inductor current.

Dimensional analysis is a great tool for checking results or developing guesses. But you have to know the underlying relationships (equations) for it to make sense. For example is newton-meters torque, or work? You can't know from just the units.

 

[gleem]

Homework Statement: What is the meaning of the area under an RC circuit's Current-Time & Voltage-Time graph while charging the Capacitor?
Relevant Equations: $$I = \frac{V}{R} \exp (\frac{-t}{RC} )$$

My logic here is purely based on units - if we integrate current on a current-time graph, the units of the integral is Amp sec which is coulombs.

Yes.

Homework Statement: What is the meaning of the area under an RC circuit's Current-Time & Voltage-Time graph while charging the Capacitor?
Relevant Equations: $$I = \frac{V}{R} \exp (\frac{-t}{RC} )$$

Another question is - what is the meaning of the area under the Voltage-Time graph represent? In this case, this would give us unit of magnetic flux (Volt sec) but is there any other meaning to this?

Yes, Volt⋅sec = weber. Another meaning is joule/amp =weber

 

[DaveE]

Yes, Volt⋅sec = weber. Another meaning is joule/amp =weber

But then why would you care about this in an RC circuit? It has a name, but does it mean anything in this system? Context matters.