Find the node voltages of the circuit

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The discussion revolves around finding node voltages in a circuit, with the book providing answers of 1 V and 2 V for v1 and v2, respectively. The original poster attempted to solve for v2 but arrived at 20 V, indicating confusion in setting up the correct equations. They were advised to focus on node analysis rather than drawing loops, emphasizing the need to calculate the algebraic sum of currents at nodes V1 and V2. Additionally, there is a query about determining the net resistance, with hints suggesting using the generator voltage and current for calculations. The conversation highlights the importance of correctly applying circuit analysis techniques to arrive at accurate results.
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Homework Statement



[PLAIN]http://img339.imageshack.us/img339/6089/electriccircuits221revi.png

Homework Equations



i = v/R

The Attempt at a Solution



My attempt at the solution is all in the red in the diagram above. Apparently the book's answers are 1 V and 2 V and it doesn't say which voltage corresponds with what but I'll assume v1 = 1 V and v2 = 2 V. When I solved for v2 with my equation I got 20 V. Can someone help me out with getting the equations set up so I can solve for the voltages? I drew the loops I used in red. Since there's 2 unknowns, I need at least 2 equations. Problem is, I don't know if my equations are correct.
 
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You calculate the algebraic sum of currents at the nodes V1 and V2. There is no sense to draw the loops, note the currents in each branch connected to the nodes V1 and V2 instead.

ehild
 
Yeah someone pointed out to me I have to do node analysis. I ended up getting the book's answer for part a. How would I find the net resistance for part b? The hint is kind of confusing me.
 
Anyone got any sort of hint for part b? It doesn't look like i can use the formula's for resistors in series and parallel here the way the circuit is set up but I may be over thinking it.
 
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The net resistance seen by the source is equal to the generator voltage divided by the generator current. Write the sum of currents at the node connected to the ground, and find the current flowing into the generator.

ehild
 
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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