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Four capacitors of 10 pF are connected in parallel with two of the capacitors having a Mylar dielectric (κ = 3) of thickness L inserted and two capacitors only separated by air at a distance L. A voltage potential of 40 V is applied across the circuit and subsequently disconnected. The Mylar dielectrics are then removed and charges are allowed to equilibrate in the system. What is the energy stored on each capacitor?
  • a)
    32000 pJ
  • b)
    64000 pJ
  • c)
    6400 pJ
  • d)
    3200 pJ
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Four capacitors of 10 pF are connected in parallel with two of the cap...
  • When four capacitors are connected in parallel, they all experience the same voltage 40V. We are interested in U, which is given by 0.5*Q2/C.
  • So what is Q? For the capacitors without the Mylar, it would be Q = CV or 400 pFV (or pC, since a coulomb = FV). For the capacitors with the Mylar, it would be Q = 3*CV or 1200 pC.
  • When the voltage potential and the Mylar dielectrics are removed, the charge in the circuit will redistribute equally to all of the different capacitors. Initially, we have 2·4 + 2·1200, so a total of 3200 pC in charge distributed among 4 capacitors. When charges are allowed to freely equilibrate, we have 800 pC on each capacitor. We can use this to find the energy stored on each capacitor.
  • Use U = 0.5*Q2 /C and we have 32000 pJ (a joule is equivalent to coulomb squared divided by farad).
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Community Answer
Four capacitors of 10 pF are connected in parallel with two of the cap...
Εr = 3.1) and the other two having a ceramic dielectric (εr = 8.5).

To find the equivalent capacitance of the parallel combination of capacitors, we can simply add up the individual capacitances.

For the capacitors with Mylar dielectric, the capacitance is given by:

C1 = C2 = 10 pF

For the capacitors with ceramic dielectric, the capacitance is given by:

C3 = C4 = 10 pF

Now, we can calculate the total capacitance:

Ctotal = C1 + C2 + C3 + C4
= 10 pF + 10 pF + 10 pF + 10 pF
= 40 pF

Therefore, the equivalent capacitance of the parallel combination of these four capacitors is 40 pF.
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Four capacitors of 10 pF are connected in parallel with two of the capacitors having a Mylar dielectric (κ = 3) of thickness L inserted and two capacitors only separated by air at a distance L. A voltage potential of 40 V is applied across the circuit and subsequently disconnected. The Mylar dielectrics are then removed and charges are allowed to equilibrate in the system. What is the energy stored on each capacitor?a)32000 pJb)64000 pJc)6400 pJd)3200 pJCorrect answer is option 'A'. Can you explain this answer?
Question Description
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