Circuit Analysis: Solving w/ Kirchoff's Laws for Potential Difference b/w a & b

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The discussion focuses on calculating the potential difference between points a and b in a circuit using Kirchhoff's laws. The user successfully solved for the current in a 2-ohm resistor but is unclear about why this resistor is relevant for determining the potential difference. Another participant suggests sharing the equations and solution to clarify the confusion. The user ultimately seeks an explanation for the relationship between the resistor's voltage and the potential difference across the specified points. Understanding this connection is crucial for grasping circuit analysis principles.
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Homework Statement



http://img185.imageshack.us/my.php?image=p2827altvk4.gif

(b) Calculate the potential difference between points a and b.

The Attempt at a Solution



I have solved the circuit using Kirchhoff's laws; I had to solve for the current in the 2 ohm resistor. But I am stuck at this question. I surmised that the potential difference would be using the 2 ohm resistor since we solved for it specifically. I found the potential difference at that resistor, and that yielded the correct answer but I have no clue why. I was wondering if someone could explain this to me? Thanks.
 
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Sheneron said:

Homework Statement



http://img185.imageshack.us/my.php?image=p2827altvk4.gif

(b) Calculate the potential difference between points a and b.


The Attempt at a Solution



I have solved the circuit using Kirchhoff's laws; I had to solve for the current in the 2 ohm resistor. But I am stuck at this question. I surmised that the potential difference would be using the 2 ohm resistor since we solved for it specifically. I found the potential difference at that resistor, and that yielded the correct answer but I have no clue why. I was wondering if someone could explain this to me? Thanks.


Not sure I understand your confusion. You solved for the voltages and currents in the circuit using KCL (most likely). That gives you the voltage across the 2 Ohm resistor and thus the current through it. Why don't you post your equations and solution, and point to what is confusing you about your final answer?
 
Well my question is why do I use the 2 ohm resistor to find the potential difference at points a and b?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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