Question

A parallel-plate air capacitor is made from two plates 0.190 m square, spaced 0.770 cm apart. It is connected to a 120 V battery. If the plates are pulled apart to a separation of 1.54 cm, suppose the battery remains connected while the plates are pulled apart.

a. What is the capacitance?
b. What is the charge on each plate?
c. What is the electric field between theplates?
d. What is the energy stored in the capacitor?

Answer 1

Answer:

aaksj

Explanation:

a) the capacitance is given of a plate capacitor is given by:

C = \epsilon_0*(A/d)

Where \epsilon_0 is a constant that represents the insulator between the plates (in this case air, \epsilon_0 = 8.84*10^(-12) F/m), A is the plate's area and d is the distance between the plates. So we have:

The plates are squares so their area is given by:

A = L^2 = 0.19^2 = 0.0361 m^2

C = 8.84*10^(-12)*(0.0361/0.0077) = 8.84*10^(-12) * 4.6883 = 41.444*10^(-12) F

b) The charge on the plates is given by the product of the capacitance by the voltage applied to it:

Q = C*V = 41.444*10^(-12)*120 = 4973.361 * 10^(-12) C = 4.973 * 10^(-9) C

c) The electric field on a capacitor is given by:

E = Q/(A*\epsilon_0) = [4.973*10^(-9)]/[0.0361*8.84*10^(-12)]

E = [4.973*10^(-9)]/[0.3191*10^(-12)] = 15.58*10^(3) V/m

d) The energy stored on the capacitor is given by:

W = 0.5*(C*V^2) = 0.5*[41.444*10^(-12) * (120)^2] = 298396.8*10^(-12) = 0.298 * 10 ^6 J

Answer 2

Answer:

a. $C=2.18*10^{-10}F$

b. $Q=2.62*10^{-8}C$

c. $E= 15584V/m$

d. $energy=3.14*10^{-2}J$

Explanation:

The question give:

• Area: $A=0.190m^{2}$

• separated distance: $d=0.770cm, d=0.0077m$

• and voltage:  $V=120volts$
• $E_{0}$ =$8.854*10^{-12}C^{2}/Nm^{2}$

a. To find the capacitance we can use

     C=$\frac{E_{0}A }{d}$     since we have d A and $E_{0}$, where

    C=$8.854*10^{-12}C^{2}/Nm^{2}*0.190m^{2}/0.0077m$

    C=$2.18*10^{-10}F$

b.To find charge we have to use:

   $Q=CV$   since

   $Q=(2.18*10^{-10}F)*(120v)$

   $Q=2.62*10^{-8}C$

c. To find electric field between the plates, that is potential difference between two plates:

    E= $\frac{V}{d}$    E= $\frac{120}{0.0077}$  

    $E= 15584V/m$

d.To find energy stored in the capacitor:

 we can use

 energy=$\frac{1}{2}$C$V^{2}$

energy=$(2.18*10^{-10}F *120^{2})/2$

energy=$3.14*10^{-2}J$