Can somebody tell my where I am going to wrong.

[dbernat32]

W=work(energy) in joules
C=capacitance in farads
A=Amperes
V=Voltage
Q=charge in coulombs
s=seconds
P=power in watts

I know that W=1/2(V^2)C is the correct formula, but I don't know how to derive it.

I am doing the following: C=Q/V, C=As/V, VC=VAs/V, VC=Ps/V, VC=W/V, W=C(V^2)
What am i missing?

--dbernat32

 

[lightarrow]

W=work(energy) in joules
C=capacitance in farads
A=Amperes
V=Voltage
Q=charge in coulombs
s=seconds
P=power in watts

I know that W=1/2(V^2)C is the correct formula, but I don't know how to derive it.

I am doing the following: C=Q/V, C=As/V, VC=VAs/V, VC=Ps/V, VC=W/V, W=C(V^2)
What am i missing?

--dbernat32

Don't know if you studied integrals.
When you add a small charge dq to a condenser at potential V and charge q, you have to make the work V*dq. But now V is not the same anylonger because V = q/C and q is now different. So you have to write V(q) and dW = V(q)*dq.
To get the total work you have to sum all these infinitesimal quantities, that is you have to compute the integral:
Integral(0;Q) V(q)*dq = Integral(0;Q) (q/c)*dq = (1/2)Q^2/C = (1/2)CV^2.
The equality coloured in blue requires knowledge of integrals.

 

[sir-pinski]

It seems like you are on the right track, but you are missing a step in the derivation. The correct formula for work (energy) in terms of capacitance, voltage, and charge is W=1/2CV^2. This can be derived by starting with the definition of capacitance, C=Q/V, and substituting it into the formula for work, W=QV. This gives you W=Q^2/V. Then, using the definition of power, P=W/t, you can substitute in the formula for work to get P=Q^2/(Vt). Finally, using the formula for current, A=Q/t, you can substitute in for Q/t to get P=AV. Rearranging this formula gives you W=1/2CV^2. So, you were on the right track, but you just needed to substitute in the definition of power and rearrange the equation to get the correct formula. Keep up the good work!