Can you explain the answer of this question below:Work done in charging a capacitor is stored in it in the form of electrostatic energy, given byA:B:C:D:The answer is a.

Question

Answer

Energy stored in a capacitor is electrical potential energy, and it is thus related to the charge Q and voltage V on the capacitor. We must be careful when applying the equation for electrical potential energy ΔPE = qΔV to a capacitor. Remember that ΔPE is the potential energy of a charge q going through a voltage ΔV. But the capacitor starts with zero voltage and gradually comes up to its full voltage as it is charged. The first charge placed on a capacitor experiences a change in voltage ΔV = 0, since the capacitor has zero voltage when uncharged. The final charge placed on a capacitor experiences ΔV = V, since the capacitor now has its full voltage V on it. The average voltage on the capacitor during the charging process is V/2, and so the average voltage experienced by the full charge q is V/2. Thus the energy stored in a capacitor, Ecap, is E( cap)=QV/2 where Q is the charge on a capacitor with a voltage V applied. (Note that the energy is not QV, but QV/2 Charge and voltage are related to the capacitance C of a capacitor by Q = CV, and so the expression for Ecap can be algebraically manipulated into three equivalent expressions:E(cap)=QV/2=C(V.V)/2 =Q.Q/2Cwhere Q is the charge and V the voltage on a capacitor C. The energy is in joules for a charge in coulombs, voltage in volts, and capacitance in farads.

Answer

W = Energy stored in the capacitor

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