Capacitors

The energy stored in a capacitor is given by (U = \frac{1}{2}CV^2), which can also be written as (U = \frac{Q^2}{2C} = \frac{1}{2}QV). All three forms are equivalent; (U = \frac{1}{2}CV^2) is most convenient when capacitance and voltage are given. The energy is stored in the electric field between the plates, with energy density (u = \frac{1}{2}\varepsilon_0 E^2). Here, (C = 5 \times 10^{-6}) F and (V = 200) V. Substituting: (U = \frac{1}{2} \times 5 \times 10^{-6} \times (200)^2 = \frac{1}{2} \times 5 \times 10^{-6} \times 4 \times 10^4 = \frac{1}{2} \times 0.2 = 0.1) J. Option 0.05 J is incorrect because it omits the factor of ((200)^2) and uses V instead of (V^2). Option 0.2 J is incorrect because it drops the factor of (1/2). Option 0.025 J is incorrect because it uses (\frac{1}{4}CV^2) instead of (\frac{1}{2}CV^2). The disconnect after charging ensures the charge remains constant. Plausibility check: 0.1 J for a 5 μF capacitor at 200 V is reasonable — a large capacitor at high voltage stores measurable energy.