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Q68PE

Expert-verifiedFound in: Page 699

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Show that for a given dielectric material the maximum energy a parallel plate capacitor can store is directly proportional to the volume of dielectric (Volume=A.d. Note that the applied voltage is limited by the dielectric strength.**

The strength saved with inside the parallel plate capacitor is without delay proportional to the volume of the dielectric.

\({U_E} \propto V\)

**Capacitance: The proportion of a system's charge change to its corresponding potential change.**

The following is the amount of energy held in a capacitor with capacitance \(C\) that is charged to a potential difference \(\Delta V\): \({U_E} = \frac{1}{2}C{(\Delta V)^2}...(1)\).

The parallel plate capacitor's capacitance is \(C = \kappa \frac{{{\varepsilon _0}A}}{d}...(2)\)

Where \(A\) is the area of each plate, \({\rm{d}}\)is the distance between them, and \({\varepsilon _0}\)is the vacuum permittivity

\(\begin{aligned}{c}{\varepsilon _0} &= 1/(4\pi k)\\ &= 8.854 \times {10^{ - 12}}{\rm{ }}{C^2}/\left( {N \times {m^2}} \right)\end{aligned}\)

Any pair of conductors separated by an insulating substance is referred to as a capacitor. When the capacitor is charged, the two conductors have charges of equal magnitude \(Q\) and opposite sign, and the positively charged conductor's potential \(\Delta V\) with respect to the negatively charged conductor is proportional to \(Q\) The ratio of \(Q\) to \(\Delta V\) determines the capacitance \(C\)

\(C = \frac{Q}{{\Delta V}}\)

And the potential difference between two points separated by a distance \(d\) in a uniform electric field of magnitude \(E\) is \(\Delta V = Ed...(3)\).

The energy stored in the parallel plate capacitor can be evaluated from Equation \((1)\):

\({U_E} = \frac{1}{2}C{(\Delta V)^2}\)

Where \(C\) the capacitance of the parallel plate capacitor is found from Equation \((2)\) and \(\Delta V\) is the potential difference across the capacitor found from Equation \((3)\):

Where \(Ad\) is the volume \(V\)of the dielectric:

The term in parenthesis is constant; therefore, the energy stored in the parallel plate capacitor is directly proportional to the volume \(V\)of the dielectric:

\({U_E} \propto V\)

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