High School

A parallel-plate capacitor has a capacitance of [tex]c_0 = 8.00 \text{ pF}[/tex] when there is air between the plates. The separation between the plates is [tex]1.90 \text{ mm}[/tex].

Option 1: [tex]4.00 \text{ pF}[/tex]
Option 2: [tex]8.00 \text{ pF}[/tex]
Option 3: [tex]16.00 \text{ pF}[/tex]
Option 4: [tex]32.00 \text{ pF}[/tex]

Choose the correct capacitance value if the dielectric between the plates is changed.

Answer :

Final answer:

The capacitance of a parallel-plate capacitor cannot be determined without knowing the area of the plates.

Explanation:

The capacitance of a parallel-plate capacitor is given by the formula C = ε0A/d, where C is the capacitance, ε0 is the permittivity of free space, A is the area of the plates, and d is the separation between the plates. In this case, the given capacitance, c0 is 8.00 pF and the separation, d, is 1.90 mm. To find the permittivity of free space, we rearrange the formula to solve for ε0: ε0 = Cd/A. Substituting the given values, we get ε0 ≈ (8.00 pF)(1.90 mm)/(A).

So we cannot calculate the permittivity of free space without knowing the area of the plates. Therefore, none of the options given (4.00 pF, 8.00 pF, 16.00 pF, 32.00 pF) can be considered as correct.

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