DC Circuit Parallel: Graph Current vs. Time

In summary, current through the inductor decreases as time goes on, while current through the resistor increases.
  • #1
Tracyxyzd
6
0

Homework Statement


There is a DC circuit with a resistor and inductor in parallel. Graph the current through the resistor vs time and the inductor vs. time.

Homework Equations


i=i(0)e^(-Rt/L)+V/R(1-e^(RT/L)

The Attempt at a Solution


My first thought was that initially current through the inductor would be 0 Amps, while current through the resistor would be V/R. At t=infinity, the inductor would become an ideal wire so all current would go through the inductor. But if that is the case then I'm not sure what the current would be since the circuit would be essentially reduced to a battery and an inductor.
 
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  • #2
Since you have not bothered to draw the circuit, I have to assume (and it's bad form to force people to make assumptions in order to answer your question) that you mean a DC voltage source with an R and an L hooked to it through a switch and you then throw the switch (closing it).

IF that is the case, then your analysis is correct so you have to ask yourself if it is actually possible to have an ideal inductor hooked directly across an ideal power source.
 
  • #3
Sorry about that. Here is the picture. They didn't include a switch, but I don't think the question makes sense otherwise. Thank you!
 

Attachments

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  • #4
Do you think that graph is correct if the elements are ideal elements? Do you really think the current through the resistor goes to zero?

You still have not answered my original question.
 
  • #5
I'm guessing it's not possible to actually have an ideal inductor hooked across an ideal power source, but I'm not sure what would actually happen. From I=V/R it would seem like infinite current, which is impossible. Since it isn't possible, then some current would have to go through the resistor the entire time. Since voltage is constant and resistance is constant, then current through the resistor would be constant. Current still increases through the inductor. If voltage across the inductor is also constant, then v=Ldi/dt givesI=vt/L, so it would be linear.
 
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  • #6
Are you sure that you have an DC source?
 
  • #7
Tracyxyzd said:
I'm guessing it's not possible to actually have an ideal inductor hooked across an ideal power source, but I'm not sure what would actually happen. From I=V/R it would seem like infinite current, which is impossible. Since it isn't possible, then some current would have to go through the resistor the entire time. Since voltage is constant and resistance is constant, then current through the resistor would be constant. Current still increases through the inductor. If voltage across the inductor is also constant, then v=Ldi/dt givesI=vt/L, so it would be linear.
It is okay to connect an inductor across a voltage source---with the proviso that you don't leave it connected for too long. (As a separate issue, there also needs to be provision made for safely disconnecting the inductor when the time comes to do so.)

Your description of the currents sounds right, so the current drawn from the source will be the sum of these and (for the time under consideration you can see it contains no exponential term).

Since you earlier attached an incorrect sketch, it would be a good idea to provide an updated sketch, to assist those others following this thread. :smile:
 
  • #8
I'm sure I have a DC circuit. Thanks for explaining what would actually happen!
 

Attachments

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  • #9
Your final graph looks good.

Would you like to have a go at explaining (using some formula) why disconnecting the inductor after some time might be dangerous?
 

FAQ: DC Circuit Parallel: Graph Current vs. Time

1. What is a DC circuit parallel?

A DC circuit parallel is a type of electrical circuit in which the components are connected in parallel to each other, meaning they share the same voltage but have different currents. This allows for multiple paths for the current to flow through, increasing the overall current capacity of the circuit.

2. How do you graph current vs. time in a DC circuit parallel?

To graph current vs. time in a DC circuit parallel, you will need to measure the current at different points in time using a multimeter or other measuring device. Then, plot these values on a graph with time on the x-axis and current on the y-axis. Repeat this process for each component in the parallel circuit to see how the currents vary over time.

3. What are the advantages of using a DC circuit parallel?

The main advantage of using a DC circuit parallel is that it allows for a higher overall current capacity compared to a series circuit. This is because the current is divided among the different components, rather than passing through each one sequentially. Additionally, if one component fails, the rest of the circuit will still function.

4. How does the total current in a DC circuit parallel compare to the individual currents in each component?

In a DC circuit parallel, the total current is equal to the sum of the individual currents in each component. This is known as Kirchhoff's Current Law, which states that the total current entering a junction must equal the total current leaving the junction.

5. What factors can affect the current in a DC circuit parallel?

The current in a DC circuit parallel can be affected by several factors, including the resistance of each component, the voltage of the power source, and the type of components used. Additionally, the overall current may also be affected by the number of components connected in parallel and their arrangement within the circuit.

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