What's the current from this circuit? Is it a short circuit or not?

[Helly123]

Homework Statement

Pic A, what's the I2?

Pic B, what's the current across a-b ?

Homework Equations

V = I*R
Voltage in series is different, the current is the same
Current in parallel is different, the voltage is the same

The Attempt at a Solution

from Pic A, I found that I1 = 1A, I3 = 1A, and V of 4ohm is 4V, V of 8ohm = 8V
it seems that 8V and I2 don't across 8ohm resistor. why?

from Pic B, I think that the current across a-b is 0A, since it's short-circuit. It's short circuit because the amount of V across 4 ohm + 1ohm the same as which across 8ohm + 2ohm. Is it right?

 

[BvU]

Your answers are correct, but your relevant equations don't seem to help you. You could study the Kirchoff laws and see if you can find useful relationships to get a complete set of equations.

For B, your argument 'since it's short circuit' doesn't hold. It's also short-circuit if one of the resistors is missing -- and in such a case there is a current flowing.

(I think you don't actually mean 'short-circuit' ...)

 

[cnh1995]

from Pic A, I found that I1 = 1A, I3 = 1A, and V of 4ohm is 4V, V of 8ohm = 8V
it seems that 8V and I2 don't across 8ohm resistor. why?

Since you know I1 and I3, you should be able to find I2 using KCL. What is your question here exactly?

from Pic B, I think that the current across a-b is 0A, since it's short-circuit. It's short circuit because the amount of V across 4 ohm + 1ohm the same as which across 8ohm + 2ohm. Is it right?

As BvU pointed out, that's not the reason why I_ab=0. Look up 'balanced Wheatstone bridge'.

 

[Helly123]

Your answers are correct, but your relevant equations don't seem to help you. You could study the Kirchoff laws and see if you can find useful relationships to get a complete set of equations.

For B, your argument 'since it's short circuit' doesn't hold. It's also short-circuit if one of the resistors is missing -- and in such a case there is a current flowing.

(I think you don't actually mean 'short-circuit' ...)

I see.. if there's current, I3 = I1 + I2
I2 = 0A
Why?

 

[cnh1995]

I see.. if there's current, I3 = I1 + I2
I2 = 0A
Why?

Because KCL tells you so.
The 8V voltage source is redundant here. You can remove it and still get the same voltages and currents everywhere in the circuit.

 

[Helly123]

For B, your argument 'since it's short circuit' doesn't hold. It's also short-circuit if one of the resistors is missing --

If 4ohm missing, the voltage drop in a-b isn't zero. So, why it's still short circuit ?
I forgot to mention that resistor in wire a-b is 0,002 ohm.
What's short circuit? When the current is 0A?

and in such a case there is a current flowing.

there is a current flowing... so it's not 0A

 

[Helly123]

Because KCL tells you so.
The 8V voltage source is redundant here. You can remove it and still get the same voltages and currents everywhere in the circuit.

But on the right side, Loop 2. The resistor is 8ohm? The I2 = 8V/8ohm = 1A (this doesn't apply?)

 

[cnh1995]

there is a current flowing... so it's not 0A

No, I2 is zero as given by KCL.

But on the right side, Loop 2. The resistor is 8ohm? The I2 = 8V/8ohm = 1A (this doesn't apply?)

It does, but the expression gives I3 and not I2. To find I2, you can use only KCL.

 

[cnh1995]

If 4ohm missing, the voltage drop in a-b isn't zero. So, why it's still short circuit ?
I forgot to mention that resistor in wire a-b is 0,002 ohm.
What's short circuit? When the current is 0A?

The solution has nothing to do with the concept of open circuit or short circuit.
If you consider the circuit as it is (without any resistor 'missing'), do you agree that I_ab=0A?
(It's actually simpler to explain why, now that you've mentioned R_ab=0.002 ohm.)

 

[Helly123]

The solution has nothing to do with the concept of open circuit or short circuit.
If you consider the circuit as it is (without any resistor 'missing'), do you agree that I_ab=0A?
(It's actually simpler to explain why, now that you've mentioned R_ab=0.002 ohm.)

I agree, but is it right?
Beside, if there's is a missing resistor before a-b make the circuit unbalanced, and the current a-b definitely not zero.

 

[cnh1995]

I agree, but is it right?
Beside, if there's is a missing resistor before a-b make the circuit unbalanced, and the current a-b definitely not zero.

Yes to both.

 

[BvU]

What's short circuit? When the current is 0A?

No. When the voltage difference is 0 V for nonzero current, no matter what the current. In other words: when the resistance is zero.