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stunner5000pt
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You have been assigned to design a transportable capacitor taht can store 250 kj of energy. You select parallel plate capactor type with a diaelectric
What is the minimum capacitor volume that is achievable using a diaelectric with strenght k?
now capacitor voluem is Area times distance between plates?
now the energy in this capactor is given by
[tex] 250 = U = \frac{1}{2} \frac{\kappa \epsilon_{0} A}{x} \Delta V^2 [/tex]
now multiplying both sides by d to make Ax = Vol
[tex] U = \frac{\kappa \epsilon_{0} Vol}{2x^2} \Delta V^2 [/tex]
now how would igo about minimizing the colume... would i differentiate by x? And set taht equal to zero? Please help!
A capacitor has 250 kJ of energy wit ha volume of 0.087 m^3. Assuming the same dielectric used in teh above question what is the diaelectric constant?
Now using the smae expressiong from the aboe question how would i figure out distance between the plates??
Have a look at my diagram for this one
A capacitor has square plates each of side a, making an angle theta with each other. Show taht for small angles theta the capacitance is given by
[tex] C = \frac{\epsilon_{0} a^2}{d} (1- \frac{a \theta}{2d} [/tex]
Hint: The capacitor may be divided into differential strips that are effectively in parallel)
now for the SQUARE plates
[tex] C = \int_{d}^{d+ a \sin{\theta}} \frac{\epsilon_{0} a^2}{x} dx [/tex]
is the integral setup correctly? It turns into
[tex] C = \epsilon_{0} a^2 \ln{(1 + \frac{a \theta}{d})} = \epsilon_{0} a^2 (\frac{a \theta}{d} - \frac{1}{2} \frac{a^2 \theta^2}{d^2} [/tex]
this doesn't look like it's heading in the right direction...
Please help! Thank you in advance!
What is the minimum capacitor volume that is achievable using a diaelectric with strenght k?
now capacitor voluem is Area times distance between plates?
now the energy in this capactor is given by
[tex] 250 = U = \frac{1}{2} \frac{\kappa \epsilon_{0} A}{x} \Delta V^2 [/tex]
now multiplying both sides by d to make Ax = Vol
[tex] U = \frac{\kappa \epsilon_{0} Vol}{2x^2} \Delta V^2 [/tex]
now how would igo about minimizing the colume... would i differentiate by x? And set taht equal to zero? Please help!
A capacitor has 250 kJ of energy wit ha volume of 0.087 m^3. Assuming the same dielectric used in teh above question what is the diaelectric constant?
Now using the smae expressiong from the aboe question how would i figure out distance between the plates??
Have a look at my diagram for this one
A capacitor has square plates each of side a, making an angle theta with each other. Show taht for small angles theta the capacitance is given by
[tex] C = \frac{\epsilon_{0} a^2}{d} (1- \frac{a \theta}{2d} [/tex]
Hint: The capacitor may be divided into differential strips that are effectively in parallel)
now for the SQUARE plates
[tex] C = \int_{d}^{d+ a \sin{\theta}} \frac{\epsilon_{0} a^2}{x} dx [/tex]
is the integral setup correctly? It turns into
[tex] C = \epsilon_{0} a^2 \ln{(1 + \frac{a \theta}{d})} = \epsilon_{0} a^2 (\frac{a \theta}{d} - \frac{1}{2} \frac{a^2 \theta^2}{d^2} [/tex]
this doesn't look like it's heading in the right direction...
Please help! Thank you in advance!
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