Resistances in Series or Parallel

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To achieve a resistance of 66.7 Ohms using three 100 Ohm resistors, the correct configuration is to connect two resistors in series (totaling 200 Ohms) and then place this combination in parallel with the third resistor. This results in an equivalent resistance of 66.7 Ohms, confirming the solution's validity. The calculation shows that the equivalent resistance of 200 Ohms in parallel with 100 Ohms yields the desired value. The discussion clarifies that this is indeed a feasible arrangement. Thus, the series-parallel combination effectively meets the resistance requirement.
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Homework Statement


You are given three identical resistors, each of 100 Ohms. Show how by using them singly or in series, parallel or series-parallel combinations you can obtain a resistance of 66.7.


Homework Equations


N/A


The Attempt at a Solution


The only way I could think of arranging the resistors in order to obtain a resistance of 66.7 Ohms was if 2 resistors connected in series were parallel to 1 resistor. Is this even possible? Or is there another solution?
 
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Why not? It is correct.
 
Well what does it work out to?

The equivalent is a 200 || 100, so that looks like it's right. All 3 || would yield 33 ohms, so ... must only be the one solution.
 
Of course it's possible (and correct, as noted). See the attached image.
 

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Well it was the only solution I could think of but I wasn't sure if I could parallel them that way. If I can then I think it's safe to assume it's correct.
 
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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