18. A parallel plate capacitor has a capacitance of 6.9 Two identical capacitors

Question

18. A parallel plate capacitor has a capacitance of 6.9

Two identical capacitors store different amounts of energy: capacitor A stores 3.6 times 10-3 J, and capacitor B stores 4.4 times 10-4 J. The voltage across the plates of capacitor B is 10 V. Find the voltage across the plates of capacitor A. A parallel plate capacitor has a capacitance of 6.9 mu F when filled with a dielectric. The area of each plate is 1.7 m2 and the separation between the plates is 9.90 times 10-6 m. What is the dielectric constant of the dielectric?

Explanation / Answer

17) Ea =CVa^2

Eb =CVb^2

Re-arrange both for C
Ea/Va^2 =C
Eb/Vb^2 =C

But, the capacitance is identical so we can equate both expressions to give:-
Eb/Vb^2 =Ea/Va^2
Solving for Va^2 gives
Va^2 = (Vb^2 x Ea)/Eb
Va = Vb x squ root of [Ea/Eb]
Va = 10 x [3.6 x 10^-3/4.4 x 10^-4]
Va = 10 x sqr root [8.18]
Va = 10 x 2.86
Va =28.6V

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