Is this correct?Oh no! Dr. Doom has just finished building his capacitor! When designing the build he decided to make the plates have an area of 10 m^2 separated by 1 mm. As the dielectric, he used strontium titanate (k = 310). Dr. Doom plans on using his battery with an EMF = 20kV connected to a set of 20 parallel 100 Mohm resistors in series to charge the capacitor.
1) How long will it take to "fully" charge the capacitor?
2) How much charge will the capacitor hold when it reaches maximum voltage?
3) How much energy is stored in the charged capacitor? How much energy is lost during the process of charging the capacitor?
C=K*e0*A/d C=310*8.85e-12*10/.001 C=2.7435e-5 F R eq=1/(20/1e8)=5e6 ohm t charge=4*R*C t charge=4*5e6*2.7435e-5 t charge=548.7 seconds, or [b]about 9 minutes[/b]. (charges to 98%)
Q=CV Q=2.7435e-5*20000 Q=[b].5487 coulombs.[/b]
PE[sub]capacitor[/sub]=1/2*Q*V PE capacitor=1/2*.5487*20000 PE capacitor=[b]5487 joules[/b]. PE dissipated=1/2*Q*V PE dissipated=[b]5487 joules[/b].