How Do You Calculate Voltmeter Readings Across Multiple Points?

[nokia8650]

See attachment.

The questions I have are finding the potential difference between A and B, between B and C, and finding the reading on a voltmeter placed between A and C.

I think that:

the potential difference between A and B is 8V.

between B and C is 4V

However, I was having trouble finding the reading on a voltmeter placed between A and C. Please can someone explain to me how to arrive at the correct answer.


Thank you.

 

[Doc Al]

What do those rectangles represent?

If you know the voltage of A with respect to B and of C with respect to B, just subtract to find the voltage between A and C.

 

[nokia8650]

The rectangles are resistors. Which do I subract from the other?

Thanks

 

[Doc Al]

Which do I subract from the other?

Doesn't matter. All you need is the magnitude of the voltage difference between them.

 

[nokia8650]

Thanks, is there any sort of formula/rule which I can use, rather than blindly subracting one from the other?

Thanks

 

[Doc Al]

All you are doing is finding the voltage difference between two points. Since you know the voltage of each with respect to a common reference (point B), all you need to do is compare them to see the difference (which is found by subtraction).

 

[Nick89]

The rectangles are probably resistors.
What are their values?

You have probably done all this already to get to the potential difference AB and BC, but just in case:

The steps you need to take to answer your question:

1. Determine the effective resistance.
2. Determine the total current (through the source) using Ohm's law.
3. Determine the current through each branch using Ohm's law (remember that a current gets split up in parallel branches, while potential does not. Potential 'splits up' between resistors.)
4. Now you know the current through each branch (which will be the same for every resistor on that branch) you can use Ohm's law (yes, again) to calculate the voltage-loss over each resistor and thus you can calculate the potential difference on each point (A, B and C).

The potential difference between A and C V_{AC} is just V_A - V_C.EDIT
Maybe you were put off by the fact that the question is asked differently.
A voltage meter is simply a device that reads the voltage difference between the two points it's connected on.
An ideal voltage meter (which you are most probably using) has an infinite input resistance which means no current is going to flow into the meter, so the network has not been changed by adding the voltage meter.

 

[nokia8650]

Thanks a lot for all the help. The resistors are meant to be identical, and so its not quite as complicated as you explained, however that was very useful help for the future. Had the resistances been not equal, how would I carry out step 3 - determining how much current was through each branch?

Thanks

 

[Nick89]

Assuming you know the total current (through the source) (let's call it I) then using Ohm's law you can calculate the current through each branch.

Let R_L be the effective resistance of the left branch and R_R the effective resistance of the right branch.
Then, I_L (current through left branch) is equal to \frac{12}{R_L} and I_R = \frac{12}{R_R}.

This is just Ohm's law: V = IR or I = \frac{V}{R}

 

[nokia8650]

ahh yes, thanks, its so obvious! I really appreciate the help!