Question:Explain why the work needed to move a particle with charge Q through a potential difference ΔV is W = QΔV, whereas the energy stored in a charged capacitor is U= 1/2Q∆V. Where does the factor 1/2 come from?
Answer:When we move a single charge q through a potential difference ∆v, its potential energy changes by qΔV.
Charging a capacitor involves moving a large number of charges from one capacitor plate to another. If ∆V is the final potential difference on the capacitor, and Q is the magnitude of the charge on each plate, the energy stored in the capacitor is
U = 1/2 Q∆V.
The factor of 1/2 is because, on average, the charges were moved through a potential difference of ½∆v
