How Do Resistors in Series and Parallel Affect Circuit Behavior?

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When identical resistors are connected in parallel, the equivalent resistance is calculated as R/n, where n is the number of resistors. Cutting a piece of copper wire with resistance R into three equal parts and connecting them in parallel results in an equivalent resistance of R/3. In a circuit with resistors in series and parallel, increasing the resistance of one resistor in parallel affects the overall current and voltage distribution in the circuit. Understanding the equations for combining resistances in series and parallel is crucial for analyzing circuit behavior. Mastering these concepts can significantly enhance one's grasp of electrical circuits.
stonnn
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i really have no clue how to do these. they seem more conceptual. any hints would be welcome! thanks!

1. Prove that when n identical resistors of resistance R are connected in parallel the equivalent resistance is R/n.

2. A piece of copper wire of resistance R is cut into 3 equal parts. When these 3 parts are connected in parallel, what is the resistance of the combination?

3. Say you have a series and parallel circuit. Resistors 2 and 3 are parallel to each other. Resistor 1 is in series with them. When you increase the resistance of 3, what happens to current and voltage values?

Thanks!
 
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hi stonn
do you know the equations for combining resistance in parallel & series?
 
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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