A parallel-plate capacitor is charged by connecting it across the terminals of a battery. If the battery remains connected and the separation between the plates is increased, what will happen to the charge on the capacitor and the voltage across it?

The voltage ( or potential difference) V increases while the charge Q decreases.

Explanation:

The capacitance C of a capacitor is defined as the measure to which the capacitor can store charges. For a parallel-plate capacitor it is given by the following relationship;

where A is the surface area of the plates, d is their distance of separation, is the permittivity of free space and is relative permittivity.

Also, the capacitance of a capacitor can be expressed in the form of equation (2)

where Q is the charge stored and V is the potential difference.

By combining (1) and (2) and making d the subject of formula, we obtain the following;

By observing (3), it is seen that the distance d of separation between the plates is directly proportional to the potential difference V and inversely proportional to the charge stored Q. This implies that an increase in the distance d of separation will bring about an increase the the voltage or potential difference V and a decrease in the charge Q.

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.

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle