How Does Kirchhoff's Law Apply to Calculating Currents and Voltage Differences?

[flyingpig]

What about the potential difference? My theory is that it is 12 - 8 = 4V because the terminals are opposite.

 

[SammyS]

After all this time?

The potential difference is equal to the voltage dropped across the 2Ω resistor.

 

[flyingpig]

The current running in the small loop is 2.545A and the bigger loop is 1.64A

So the current running through the 2Ω resistor is 0.908A.

So now you want me to 2Ω * 0.908A = 1.82V because this is the only resistor that intercepts both loops.

But I don't like this answer. Does it matter where a and b are placed?

 

[SammyS]

The current running in the small loop is 2.545A and the bigger loop is 1.64A

So the current running through the 2Ω resistor is 0.908A.

So now you want me to 2Ω * 0.908A = 1.82V because this is the only resistor that intercepts both loops.

But I don't like this answer. Does it matter where a and b are placed?

I thought we called these I_a & I_b.

If you want the answer, then you should want to: 2Ω * 0.908A = 1.82V .

As long as a is to the left of the batteries and the 2Ω resistor & b is to the right of all the resistors, their exact location doesn't matter.

 

[flyingpig]

But why is 12V - 8V wrong?

 

[SammyS]

For the same reason that any other wrong answer is wrong.

There is no reason the answer should be 12V - 8V.

 

[flyingpig]

But was my guess at what the answer really should have been right when you hinted at me? That it is the voltage drop across the 2Ω resistor because the 2Ω resistor is the only resistor in the intersection of the loop?

 

[SammyS]

But was my guess at what the answer really should have been right when you hinted at me? That it is the voltage drop across the 2Ω resistor because the 2Ω resistor is the only resistor in the intersection of the loop?

Yes.

As long as you got I_a & I_b right.

 

[flyingpig]

Sammy, the solutions posted said the voltage drop is -1.80V

Here is my question, when we tackle these problems, aren't we only concerned with the magnitude?

 

[SammyS]

Sammy, the solutions posted said the voltage drop is -1.80V

Here is my question, when we tackle these problems, aren't we only concerned with the magnitude?

No. Among other things, the sign has to do with which way the current flows.

 

[flyingpig]

Then how do I know that it is -1.80V?

 

[SammyS]

The sign will depend upon whether they found V_a - V_b or V_b - V_a.

 

[flyingpig]

So it is not unique?