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Two round disks, each with a 0.5 cm diameter are spaced 2 mm apart. Batman conne

ID: 1372933 • Letter: T

Question

Two round disks, each with a 0.5 cm diameter are spaced 2 mm apart. Batman connects these two disks to opposite terminals of a compact 65,000 V experimental battery he has borrowed from Stark Industries, and thus forms a powerful capacitor. Batman then disconnects this battery, leaving the plates of his capacitor charged.

A) Suppose Batman needs to decrease his capacitance on the capacitor so he places a dielectric constant of 36.4 between the plates, what is the capacitance of Batman's MODIFIED capacitor?

B) What is the new potential difference between the modified plates? (Show equation, variables and steps)

C) What is the charge on Batman's modified capacitor?

D) What is the electric potential energy on Batman's modified capacitor? (Show equation, variables and steps)

E) The energy stored in Bat Man's modified capacitor is discharged over 0.5 millisconds. Find the average power of Bat Man's modified capcitor.

Explanation / Answer

Beforce placing dilectric between the plates,

r = d/2 = 0.5 cm/2 = 0.25 cm = 0.0025 m

A = pi*r^2 = pi*0.0025^2 = 1.96*10^-5 m^2

d = 2*10^-3 m

Capaciatance of a parallel plate capacitor, Co = A*epsilon/d

= 1.96*10^-5*8.854*10^-12/(2*10^-3)

= 8.68*10^-14 F

charge on the capacitor, Qo = Co*Vo

= 8.68*10^-14*65000

= 5.64*10^-9 C

A) when dilectric is placed between the plates, C = K*Co

= 36.4*8.68*10^-14

= 3.16*10^-12 F <<<<-----Answer

B) charge remains same. so

Q = Qo

C*V = Co*Vo

k*Co*V = Co*Vo

==> v = Vo/k

= 65000/36.4

= 1785.7 volts <<<<-----Answer


C) same, Q = Qo = 5.64*10^-9 C <<<<-----Answer


D) potentail enrgy stored in capaciotr,
U = Q^2/(2*C)

= Qo^2/(2*k*Co)

= 1.83*10^-4/(36.4)

= 5.03*10^-6 J <<<<-----Answer


E) power = the rate of enrgy discharged

= dU/dt

= 5.03*10^-6/(0.5*10^-3)

= 1.006*10^-2 Watts <<<<-----Answer

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