Engineering Understanding KVL and KCL for Circuit Analysis

[carlodelmundo]

Homework Statement

Basically, find V_ab

[PLAIN]http://carlodelmundo.com/hw/circuit.png

Is this correct -- note: please tell me that my methodology is sound; DO NOT GIVE ME A NUMERICAL ANSWER.

The problem asks for V_AB. What's weird to me is that there is a potential across two terminals? (The weird part is: the terminals are connected to another voltage source!)

I used KVL... and I'm fairly accurate that my calculation is correct. However, I am confused with finding the actual V_AB. Can I simply apply Ohm's law, and "lump" all of the resistors into one resistor (composition?) Would V_AB be equivalent to the sum of all the voltages (taking polarities into account)?

 

[Zryn]

Your current calculations look good, but I think Vab is wrong. Keep in mind Vab = Va - Vb i.e. the voltage between two different points. As you have done in the first part of your current equations, all the voltage 'gains' must equal all of the voltage 'drops' (Kirchoffs Voltage Law) in the loop, but Vab doesn't include all of the resistances in the loop.

The terminals can be disregarded also, since they merely represent a connection point, but with or without them the circuit is the same.

Check out this redrawn circuit.

 

[carlodelmundo]

I see. Based on your chart, I may have gained some insight. Let me clarify-- so we're not supposed to use all of the resistances in the circuit?

Is it correct to assume that to calculate V_ab, I may simply just find the potential difference between V_a and V_b?

e.g.: according your chart, V_ab = v_r3 + V_4v = 3(i) + 4 = 3(16/6) + 4 = 12V? If this is true, can I solve for the reverse and negate the answer? (the other resistors and other voltage source)

 

[tiny-tim]

hi carlodelmundo!

Zryn is offline, so I'll confirm that 12 V is correct …

you calculated it via the 4 V, but if you'd gone the other way, that will give the same result …

try it and see (you've probably already done so)!

the whole point of KVL is that the potential differences (for want of a better phrase) all add to zero around a loop …

when you're asked for the potential between two points, it's exactly the same as the sum of the voltages you'd use in KVL itself

 

[carlodelmundo]

Thanks! this makes a lot of sense now!