Which equation represents the total energy stored in a capacitor?

Which equation represents the total energy stored in a capacitor?

• A. energy = LI^2/2
• B. energy = CV^2/2
• C. energy = Q^2/2C
• D. Both energy = CV^2/2 and energy = Q^2/2C

Answer: (D)

The total energy stored in a capacitor can be expressed in multiple equivalent forms, which is why the correct answer includes both energy = CV^2/2 and energy = Q^2/2C. The first equation, energy = CV^2/2, is derived from the fundamental relationship between capacitance (C), voltage (V), and the energy stored in a capacitor. In this context, the energy stored is shown to be proportional to the capacitance and the square of the voltage across the capacitor. This reflects the work done to charge the capacitor to voltage V through the equation that defines capacitance as C = Q/V, where Q is the charge stored in the capacitor. The second equation, energy = Q^2/2C, is equally valid and is derived from the fundamental relationships involving charge, capacitance, and energy storage. Here, the energy is expressed directly in terms of the charge (Q) stored in the capacitor and the capacitance (C). By substituting the expression for voltage (V = Q/C) into the first equation, one can arrive at this second formulation. Thus, both equations represent the same quantity of energy stored in the capacitor in different terms (one in voltage and one in charge),

The total energy stored in a capacitor can be expressed in multiple equivalent forms, which is why the correct answer includes both energy = CV^2/2 and energy = Q^2/2C.

The first equation, energy = CV^2/2, is derived from the fundamental relationship between capacitance (C), voltage (V), and the energy stored in a capacitor. In this context, the energy stored is shown to be proportional to the capacitance and the square of the voltage across the capacitor. This reflects the work done to charge the capacitor to voltage V through the equation that defines capacitance as C = Q/V, where Q is the charge stored in the capacitor.

The second equation, energy = Q^2/2C, is equally valid and is derived from the fundamental relationships involving charge, capacitance, and energy storage. Here, the energy is expressed directly in terms of the charge (Q) stored in the capacitor and the capacitance (C). By substituting the expression for voltage (V = Q/C) into the first equation, one can arrive at this second formulation.

Thus, both equations represent the same quantity of energy stored in the capacitor in different terms (one in voltage and one in charge),