Question

An inductor is connected in series to a fully charged capacitor. Which of the following statements are true? Check all that apply.

- As the capacitor is charging, the current is increasing.

- The stored electric field energy can be greater than the stored magnetic field energy.

- As the capacitor is discharging, the current is increasing.

- The stored electric field energy can be less than the stored magnetic field energy.

- The stored electric field energy can be equal to the stored magnetic field energy.

Answer 1

Concepts and reason

The concept of inductance, capacitance and energy in series LC circuit is required to answer the question.

First, determine the total energy stored in a series LC circuit. Then, identify the incorrect statement using the concepts energy stored in a capacitor and inductor. Finally, find out the correct statements.

Fundamentals

The energy stored in an inductor is given as,

${E_L} = \frac{1}{2}L{I^2}$

Here, L is the inductance and I is the current through the inductor.

The energy stored in a capacitor is given as,

${E_C} = \frac{1}{2}C{V^2}$

Here, C is the capacitance and V is the voltage across the capacitor.

(1)

The total energy stored in the LC circuit is the sum of the energy stored in capacitor and energy stored in inductor. That is,

$E = {E_L} + {E_C}$

Substitute $\frac{1}{2}L{I^2}$ for ${E_L}$ and $\frac{1}{2}C{V^2}$ for ${E_C}$ in equation $E = {E_L} + {E_C}$ as follows:

$E = \frac{1}{2}L{I^2} + \frac{1}{2}C{V^2}$

Total energy always remains conserved. The charging of capacitor means that the charge stored in the capacitor is increasing and so there is increase in the energy stored in the capacitor. The total energy will remain conserved only if the energy stored in the inductor decreases and this can be done by decreasing the current.

Hence, the statement that, as the capacitor is charging, current is increasing is false.

(2)

The total energy stored in the LC circuit is given as,

$E = \frac{1}{2}L{I^2} + \frac{1}{2}C{V^2}$

Here, the first term indicates the stored magnetic field energy in the inductor and the second term indicates the stored electric field energy in the capacitor. These two energies are independent.

Therefore, the stored electric field energy can be greater than the stored magnetic field energy, but the total energy must remain constant.

(3)

The total energy stored in the LC circuit is given as,

$E = \frac{1}{2}L{I^2} + \frac{1}{2}C{V^2}$

Total energy always remains conserved. The discharging of capacitor means that the charge stored in the capacitor is decreasing and so there is decrease in the energy stored in the capacitor. The total energy will remain conserved only if the energy stored in the inductor increases and this can be done by increasing the current.

Hence, the current is increasing as the capacitor is discharging.

(4)

The total energy stored in the LC circuit is given as,

$E = \frac{1}{2}L{I^2} + \frac{1}{2}C{V^2}$

Here, the first term indicates the stored magnetic field energy in the inductor and the second term indicates the stored electric field energy in the capacitor. These two energies are independent and can be less than, greater than or equal to each other.

Therefore, the stored electric field energy can be less than the stored magnetic field energy, but the total energy must remain constant.

(5)

The total energy stored in the LC circuit is given as,

$E = \frac{1}{2}L{I^2} + \frac{1}{2}C{V^2}$

The first term in the above expression indicates the stored magnetic field energy in the inductor and the second term indicates the stored electric field energy in the capacitor. These two energies are independent and can be less than, greater than or equal to each other, but the total energy must remain constant.

Therefore, the stored electric field energy can be equal to the stored magnetic field energy, but the total energy must remain constant.

Ans: Part 1

The given statement is false.

Part 2

The given statement is true.

Part 3

The given statement is true.

Part 4

The given statement is true.

Part 5

The given statement is true.