# 19.5 Capacitors and dielectrics  (Page 6/12)

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## Phet explorations: capacitor lab

Explore how a capacitor works! Change the size of the plates and add a dielectric to see the effect on capacitance. Change the voltage and see charges built up on the plates. Observe the electric field in the capacitor. Measure the voltage and the electric field.

## Section summary

• A capacitor is a device used to store charge.
• The amount of charge $Q$ a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
• The capacitance $C$ is the amount of charge stored per volt , or
$C=\frac{Q}{V}.$
• The capacitance of a parallel plate capacitor is $C={\epsilon }_{0}\phantom{\rule{0.15em}{0ex}}\frac{A}{d}$ , when the plates are separated by air or free space. ${\epsilon }_{\text{0}}\phantom{\rule{0.25em}{0ex}}$ is called the permittivity of free space.
• A parallel plate capacitor with a dielectric between its plates has a capacitance given by
$C={\mathrm{\kappa \epsilon }}_{0}\phantom{\rule{0.25em}{0ex}}\frac{A}{d},$
where $\kappa$ is the dielectric constant of the material.
• The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.

## Conceptual questions

Does the capacitance of a device depend on the applied voltage? What about the charge stored in it?

Use the characteristics of the Coulomb force to explain why capacitance should be proportional to the plate area of a capacitor. Similarly, explain why capacitance should be inversely proportional to the separation between plates.

Give the reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. What is the independent reason that a dielectric material also allows a greater voltage to be applied to a capacitor? (The dielectric thus increases $C$ and permits a greater $V$ .)

How does the polar character of water molecules help to explain water’s relatively large dielectric constant? ( [link] )

Sparks will occur between the plates of an air-filled capacitor at lower voltage when the air is humid than when dry. Explain why, considering the polar character of water molecules.

Water has a large dielectric constant, but it is rarely used in capacitors. Explain why.

Membranes in living cells, including those in humans, are characterized by a separation of charge across the membrane. Effectively, the membranes are thus charged capacitors with important functions related to the potential difference across the membrane. Is energy required to separate these charges in living membranes and, if so, is its source the metabolization of food energy or some other source? The semipermeable membrane of a cell has different concentrations of ions inside and out. Diffusion moves the K + (potassium) and Cl – (chloride) ions in the directions shown, until the Coulomb force halts further transfer. This results in a layer of positive charge on the outside, a layer of negative charge on the inside, and thus a voltage across the cell membrane. The membrane is normally impermeable to Na + (sodium ions).

## Problems&Exercises

What charge is stored in a $\text{180 µF}\phantom{\rule{0.25em}{0ex}}$ capacitor when 120 V is applied to it?

$\text{21}\text{.}6\phantom{\rule{0.25em}{0ex}}\text{mC}$

Find the charge stored when 5.50 V is applied to an 8.00 pF capacitor.

What charge is stored in the capacitor in [link] ?

$\text{80}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{mC}$

Calculate the voltage applied to a $2\text{.}\text{00 µF}$ capacitor when it holds $3\text{.}\text{10 µC}$ of charge.

What voltage must be applied to an 8.00 nF capacitor to store 0.160 mC of charge?

20.0 kV

What capacitance is needed to store $3\text{.}\text{00 µC}$ of charge at a voltage of 120 V?

What is the capacitance of a large Van de Graaff generator’s terminal, given that it stores 8.00 mC of charge at a voltage of 12.0 MV?

$\text{667}\phantom{\rule{0.25em}{0ex}}\text{pF}$

Find the capacitance of a parallel plate capacitor having plates of area $5\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ that are separated by 0.100 mm of Teflon.

(a)What is the capacitance of a parallel plate capacitor having plates of area ${\text{1.50 m}}^{2}$ that are separated by 0.0200 mm of neoprene rubber? (b) What charge does it hold when 9.00 V is applied to it?

(a) $4\text{.}\text{4 µF}$

(b) $4\text{.}0×{\text{10}}^{–5}\phantom{\rule{0.25em}{0ex}}\text{C}$

Integrated Concepts

A prankster applies 450 V to an $\text{80}\text{.}0 µF$ capacitor and then tosses it to an unsuspecting victim. The victim’s finger is burned by the discharge of the capacitor through 0.200 g of flesh. What is the temperature increase of the flesh? Is it reasonable to assume no phase change?

Unreasonable Results

(a) A certain parallel plate capacitor has plates of area ${\text{4.00 m}}^{2}$ , separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?

(a) 14.2 kV

(b) The voltage is unreasonably large, more than 100 times the breakdown voltage of nylon.

(c) The assumed charge is unreasonably large and cannot be stored in a capacitor of these dimensions.

Pls guys am having problem on these topics: latent heat of fusion, specific heat capacity and the sub topics under them.Pls who can help?
Thanks George,I appreciate.
hamidat
this will lead you rightly of the formula to use
Abolarin
Most especially it is the calculatory aspects that is giving me issue, but with these new strength that you guys have given me,I will put in my best to understand it again.
hamidat
you can bring up a question and let's see what we can do to it
Abolarin
the distance between two suasive crests of water wave traveling of 3.6ms1 is 0.45m calculate the frequency of the wave
v=f×lemda where the velocity is given and lends also given so simply u can calculate the frequency
Abdul
You are right my brother, make frequency the subject of formula and equate the values of velocity and lamda into the equation, that all.
hamidat
lExplain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.
When light is reflected at Brewster's angle from a smooth surface, it is 100% polarizedparallel to the surface. Part of the light will be refracted into the surface.
Ekram
What is specific heat capacity?
Specific heat capacity is the amount of heat required to raise the temperature of one (Kg) of a substance through one Kelvin
Paluutar
formula for measuring Joules
I don't understand, do you mean the S.I unit of work and energy?
hamidat
what are the effects of electric current
What limits the Magnification of an optical instrument?
Lithography is 2 micron
Venkateshwarlu
what is expression for energy possessed by water ripple
what is hydrolic press
An hydraulic press is a type of machine that is operated by different pressure of water on pistons.
hamidat
what is dimensional unite of mah
i want jamb related question on this asap🙏
What is Boyles law
it can simple defined as constant temperature
Boyles law states that the volume of a fixed amount of a gas is inversely proportional to the pressure acting on in provided that the temperature is constant.that is V=k(1/p) or V=k/p
what is motion
getting notifications for a dictionary word, smh
Anderson
what is escape velocity
the minimum thrust that an object must have in oder yo escape the gravitational pull
Joshua
what is a dimer
Mua
what is a atom
how to calculate tension
what are the laws of motion
Mua By By   By  By  By   By