Why is the 10 μF capacitor causing extreme confusion?

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The discussion revolves around confusion regarding the notation and implications of a 10 μF capacitor in a circuit problem. Participants clarify that 10^-5 should indeed be interpreted as 10 μF, not 10^-6. There is debate over whether the inequality sign should be used, with some agreeing that it should reflect the maximum voltage each capacitor can withstand. The key takeaway is that in a series circuit, the capacitor with the lowest capacitance experiences the highest voltage, which is crucial for calculating charge and voltage distribution among the capacitors. This understanding helps resolve the initial confusion surrounding the problem.
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Homework Statement



[PLAIN]http://img27.imageshack.us/img27/6946/unledyh.png


My question is

1) What in the world is 10^-5 ? Shouldn't it be 10^-6?
2) I know they already explained why it is the 10uF Capacitor, but could someone massage it further for me? I am an idiot

Also, I know I being picky, but shouldn't it be an inequality sign of \leq
 
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1) 10-5 = 10 × 10-6. I presume the units should be μF. I'd take a point from the person writing the solutions. LOL !

It's an equal sign because they asked for the maximum.

Added in Edit:

After more carefully reading the statement about the capacitors, I agree that the answer should have the inequality you suggested.

It doesn't say that can each withstand 100V, it says none can withstand more than 100V.
 
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I would approach this a bit differently.

Since the capacitors are in series, each will have the same charge. Therefore, the one with the least capacitance (the 10 μF capacitor) will have the greatest voltage (potential) across it, namely 100 Volts. Use this to find the charge on the 10 μF capacitor, and thus each of the others. Then find the voltage across each of them and take the sum.
 
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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