Question

For an lc circuit, when the charge on the capacitor is one-half of the maximum charge, the energy stored in the capacitor is?.

Answer 1

The energy stored in a capacitor in an LC circuit when the charge is one-half the maximum is one-fourth of the maximum energy. This results from the energy being proportional to the square of the charge on the capacitor.

Step-by-step explanation:

For an LC circuit, when the charge on the capacitor is one-half of the maximum charge, the energy stored in the capacitor is not simply one-half of the maximum energy. Energy stored in a capacitor, given by the formula U = (1/2)CV2, is proportional to the square of the charge q on the capacitor at any instant. The relationship between the charge q, the maximum charge Q, and the capacitance C is q = CV, and the maximum charge Q is associated with the maximum voltage Vmax.

Therefore, when the charge is at one-half of its maximum value (q = Q/2), the energy stored in the capacitor Uc at that instant is (1/2)C(V/2)2 = (1/2)C(Q/2C)2 = (1/2)(Q2/4C) = Q2/8C. This means the energy is one-fourth of the maximum energy, considering that the maximum energy is Umax = (1/2)(Q2/C).