What Is the Voltage Between Terminals A and B?

[Learnphysics]

Homework Statement

[PLAIN]http://img80.imageshack.us/img80/6128/1036t.png

Homework Equations

V=IR

Kirchoff's voltage law

Kirchoff's current law

voltage divider

The Attempt at a Solution

The soloution for v1 and v2 come easily, just a matter of recognizing that there is no current flowing from the 15v source to terminal a, so, the 8ohm and 7 ohm are essentially in series and voltage divider can be applied

In the same way we can solve for v2 by using V= IR, 2*2 =4v.

However voltage between a and b has had me stumped for literally more than an hour. I'v had my attempts at trying to find the thevenin equivalent resistance and the closed circuit current and using these finding the open circuit voltage, but they have not worked.

 

[ehild]

Does any current flow through the 6 ohm resistor?

ehild

 

[Learnphysics]

Does any current flow through the 6 ohm resistor?

ehild

I have a feeling it doesn't but again I'm not complete sure.

Current doesn't flow through because there's no path for it to return to the voltage source.

But perhaps the current can flow into the negative of the current source (do current sources even have terminals?

I'v tried to do source transformation on the current source, which turned it into a 4V voltage source, and also made the 2ohm resistance in parralell with it change to be in series with it.

I believe that with this transformation current would flow through the 6 ohm resistor as there would be a difference in voltage. Have i gone wrong somewhere?

 

[ehild]

The current sources just produce current, but you can not say the voltage across them if they are not connected into a circuit.

You are right, there is no closed path with the 6 ohm resistor included. If it enters into the current source, how does it go further? The current has to return to the original starting point, and cannot cross itself or travel twice along the same path. If there is no current through the resistor, there is no potential drop across it. So its terminals are at equal potentials.

ehild

 

[Learnphysics]

The current sources just produce current, but you can not say the voltage across them if they are not connected into a circuit.

You are right, there is no closed path with the 6 ohm resistor included. If it enters into the current source, how does it go further? The current has to return to the original starting point, and cannot cross itself or travel twice along the same path. If there is no current through the resistor, there is no potential drop across it. So its terminals are at equal potentials.

ehild

Ok, so if there is no current flowing through that 6 ohm resistor, (and because there's no current there;s no voltage drop across it). what i should be doing is finding the voltage at terminal a and subtract it from the voltage at terminal b. To get the voltage between them.

the voltage at terminal a, will be EQUAL to the voltage at the node to the right of the 8 ohm resistor (because there is no voltage drop across the 3 ohm resistor as there's no current through it).

I know the current i1 = 1Ampere. and i know that (15V(source) - Va)/8 = 1ampere.
because of V/r = I

I get 7V for Va.

How would i attempt to find the voltage at terminal B, because it's there's a current source/rather than voltage source, I'm a little confused on how to proceed.

EDIT:

ah, i see. i can use my source transformation to turn the 2A source into a 4V source. this will make terminal b be at 4V. And the difference across a and b will be 3V. As the textbook's answers says.

Could you confirm if i'v done this right? Or if is it a coincidentally right answer?

 

[ehild]

It is completely all right. :) ehild