Just In Time Question 2 Satisfied with her previous experiment in the vacuum cha

Question

Just In Time Question 2 Satisfied with her previous experiment in the vacuum chamber, Prof. Marcia Grail needs to store a great deal of launch her next attempt at world domination. She decides to store this energy in a gigantic parallel plate capacitor of the plates fixed, and the distance between the plates minutely tunable. This capacitor i the previous, and the atmosphere removed. If the capacitance i voltage would need to be applied? If it takes a day to charge, then how much power is required (in MW)? energy in order to with the area s placed in the vacuum chamber from s 0.01 Farad, and is meant to store an energy of 20 GJ, then what

Explanation / Answer

Energy to be stored in the capacitor, E = 20 GJ = 20 x 10^9 J

Now the expression for the energy in a capcitor, E = (1/2)*C*V^2

given that, C = 0.01 F

put the value in the above expression -

20 x 10^9 = (1/2)*0.01*V^2

=> V^2 = 2x20x10^9 / 0.01 = 2x20x10^11 = 4 x 10^12

=> V = sqrt[4 x 10^12] = 2 x 10^6 Volt = 2000 kV.

So, voltage needed to be applied = 2000 kV

Calculate in number of seconds in a day.

This is 24x60x60 sec.

Let us assume that the requisite power is P to charge the capacitor.

So, we have -

P x 24x60x60 = 20 x 10^9 J

=> P = (20x10^9) / (24x60x60) = 231481 W = 231.48 kW.

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