Physics, 15.07.2021 19:20 Riplilpeep

Define capacitance of a parallel plate capacitor and state one application of it in electric circuit?

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Answer from: supreme18

The capacitance of a parallel plate capacitor is the quantity of charge the capacitor can hold.

This capacitance is proportional to the area of the any of the two plates (if the area of the plates are the same), or the smaller of the two plates (if the plates have different areas) and inversely proportional to the square of the distance of separation (or thickness of the dielectric material) between the plates. It is mathematically expressed as;

C = Aε₀ / d

Where;

C = capacitance

A = Area of one of the plates.

d = distance between the plates

Some of the applications of capacitance (or simply a capacitor) in an electric circuit are;

i. For storage of electrostatic energy.

ii. For filtering and tuning of circuits.

Answer from: Quest

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

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

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

Answer from: Quest

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