Electricity and Magnetism

Capacitors and Transformers

Capacitors

         

The two metal plates in the above figure have net charges of +140.0 pC+140.0\text{ pC} and 140.0 pC,-140.0\text{ pC}, respectively. If the potential difference between them is 10.0 V,10.0\text{ V}, what is the capacitance of the system consisting of the two metal plates?

The capacitor in the above figure has a capacitance of 40.0μF40.0 \,\mu\text{F} and is initially uncharged. The battery provides a potential difference of 90.0 V.90.0\text{ V}. After switch S is closed, how much charge will pass through it?

Consider a spherical capacitor which consists of two concentric spherical shells of radii 38.0 mm38.0\text{ mm} and 40.0 mm,40.0\text{ mm}, respectively. If we want to make a parallel-plate capacitor with the same separation, what must be the area of each plate for the same capacitance?

The value of electrostatic constant is k=14πε0=8.99×109 Nm2/C2\displaystyle k=\frac{1}{4\pi\varepsilon_0}=8.99 \times 10^9 \text{ N}\cdot\text{m}^2\text{/C}^2 and the value of the permittivity constant is ε0=8.85×1012 C2/Nm2.\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.

One can make a homemade capacitor using an aluminum foil and a plastic or a wooden stick (it's important that the stick is an insulator). Make a small ball out of the aluminum foil and wrap it around the stick. Then make a wider foil sphere around the ball so that they don't touch, and your capacitor is ready!

If the radius of the smaller ball is 5 cm5~\mbox{cm} and of the bigger sphere 15 cm 15~\mbox{cm}, which capacitance in pF do you expect to obtain?

Details and assumptions

  • The ball and the sphere are centered around the same point

If you want to make a parallel-plate capacitor of capacitance 0.9 pF0.9\text{ pF} with two metal plates with area 1.1 cm2,1.1\text{ cm}^2, what must be the separation between the two plates?

The value of the permittivity constant is ε0=8.85×1012 C2/Nm2.\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.

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