Electrical Engineering: What is the current through this?

[Boltzman Oscillation]

Homework Statement

I have a current source of 2mA in parrallel with a resistor of 9.2kOhm and a short. What is the current through the short?

Homework Equations

The Attempt at a Solution

I always thought shorts had an infinite amount of current but maybe I do not quite understand the concept. Perhaps by infinite it means that it draws all of the current? So the current through the resistor would be really small while the current through the short will be the maximum allowed aka 2mA in this case? is this correct?

 

[berkeman]

I have a current source of 2mA

A current source sources the specified current, regardless of the impedance it is driving (at least for ideal current sources)...

 

[anorlunda]

You know how to combine resistances in parallel. Think of your problem as RA in parallel with RB. Write the expression for the parallel combination. What does that tell you?

 

[Boltzman Oscillation]

You know how to combine resistances in parallel. Think of your problem as RA in parallel with RB. Write the expression for the parallel combination. What does that tell you?

Hmm so I would place in parrallel the 9.2kOhm resistor with a short. A short has an infinite resistance so i would end up getting a total resistance of 0?

1/((1/inf) + (1/9.2k))?
1/inf is zero so i get Rt = 9200Ohm. What does this tell me about the current through the short though?

 

[anorlunda]

A short has an infinite resistance

Care to try again?

 

[Boltzman Oscillation]

Care to try again?

oops a short has no resistance. So 1/((1/0) + (1/9.2k)) is zero. So the total resistance of the circuit is zero? What does this say about the current through the short?

 

[berkeman]

What does this say about the current through the short?

Did you see my reply in post #2?

 

[Boltzman Oscillation]

Did you see my reply in post #2?

I see what you mean but wouldn't the current split between the resistor branch and the short circuit branch? In this case a short circuit draws most of the current and thus the current passing through the short is equal to the current source?

 

[bartman_bartman]

So you have 3 parallel branches: 2 mA current source, 9.2Kohm resistor, and a short. A perfect current source means it produces A FIXED CURRENT (2 mA in this case) but the voltage can vary, depending on the load you attach to it. Assuming your short has 0 ohms, all the current (2 mA) will go through the short, 0 mA will go through the 9.2K. So you won't have infinite current because your perfect current source produces exactly 2.5 mA... no more, no less.

You would only get infinite current if you had a perfect voltage source in parallel with the short. The perfect voltage source produces a FIXED VOLTAGE, but supplies whatever current is necessary, depending on the load attached to it.

<< Small deletion by a Mentor >>

 

[berkeman]

I see what you mean but wouldn't the current split between the resistor branch and the short circuit branch? In this case a short circuit draws most of the current and thus the current passing through the short is equal to the current source?

Yep! A current divider depends on the relative resistance between the legs. If one leg has zero resistance, it takes all of the current.

 

[CWatters]

I always thought shorts had an infinite amount of current but maybe I do not quite understand the concept.

If you put a short across a _voltage_ source then the current is infinite. The voltage is determined by the voltage source and the current is determined by the total resistance. I=V/R and R=0 so I=infinite.

However in your OP you have a _current_ source. A current source determines the current. The voltage is determined by the total resistance. V=IR and R=0 so V=0.Golden rules of electronics..

Never short an ideal voltage source.
Never open circuit an ideal current source.

 

[Tom.G]

I see what you mean but wouldn't the current split between the resistor branch and the short circuit branch? In this case a short circuit draws most of the current and thus the current passing through the short is equal to the current source?

To get a current thru a resistance there must be a voltage across it; so in the Real World, yes there would be some small current thru the resistor.

However In your example you have a resistor in parallel with an ideal short.

You have already determined the current thru the short and the resistance of the short. Using V= I⋅R with the current source and the resistance of the short, what is the voltage across the short, and consequently across the resistor?

Cheers,
Tom

 

[Delta2]

Just to do this with Kirchoff's laws though it has been qualitatively explained by @berkeman and others

KCL : ##I=I_R+I_S (1)## WHERE ##I_R## the resistor current and ##I_S## the short circuit current.
KVL: ##I_RR+I_S0=0\Rightarrow I_RR=0\Rightarrow I_R=0##

hence from (1) we get that the total current ##I=I_S## passes through the short.

A note : To be able to conclude that ##I_R=0## from KVL, we need the assumption that ##I_S## will be finite, which is true if we have a current source but it is not true if we have a voltage source.