How Is Energy Calculated in a Charged Capacitor?

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The discussion revolves around calculating the energy stored in a charged capacitor and the additional energy required to increase its voltage. The energy stored in a 4.7 microfarad capacitor charged to 290 V is calculated using the formula U = 1/2 * C * V^2, resulting in approximately 0.1975 J. For the second part, the user attempts to find the additional energy needed to charge the capacitor from 290 V to 780 V but encounters errors in their calculations. They express confusion about the correct method for determining the change in energy and seek clarification on their approach. The conversation highlights the importance of accurately applying formulas and understanding energy changes in capacitors.
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Homework Statement



1) A 4.7-mu or micro FF capacitor is charged to 290 V. How much energy is stored in the capacitor?

2) How much additional energy is required to charge the capacitor from 290 V to 780 V?

Homework Equations



U = 1.2*C*V2



The Attempt at a Solution



The first one I got right...

1) U = 1/2*(4.7 * 10-6)*290 = 1.975E-1

2) I thought to find this one you could use the change in energy would have to equal the change in potential? So I tried this...but its not right, can anyone tell me where I went wrong? thanks!

Uf - 1.975E-1 = .5*(4.7E-6)(780)2 - .5*4.7E-6*2902

Uf = 1.4297 J
 
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I did Uf - 1.975E-1 = .5*(4.7E-6)(780)2 - .5*4.7E-6*290^2

but I got 1.232
 
Last edited:

Thread 'Errors and significant figures'

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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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