The power dissipated in a resistor is given by p = v 2 / r , which means power decreases if resistance increases. yet this power is also given by p = i 2r , which means power increases if resistance increases. explain why there is no contradiction here?

Explanation:

Power Dissipated in a resistor is given by two methods i.e.

 and

where

both formula gives Power but Former is used when voltage is constant i.e. when resistors are in parallel and the later is used when the resistor are in series .

Though can also be used in series but we have to calculate the Potential drop across each resistor then we can apply the formula.

Similar is with

First we have to calculate current through each resistor then we can apply the Formula

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y