Question

In: Physics

An inductor is connected in series to a fully charged capacitor. Which of the following statements...

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.


Solutions

Expert Solution

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,

EL=12LI2{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,

EC=12CV2{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=EL+ECE = {E_L} + {E_C}

Substitute 12LI2\frac{1}{2}L{I^2} for EL{E_L} and 12CV2\frac{1}{2}C{V^2} for EC{E_C} in equation E=EL+ECE = {E_L} + {E_C} as follows:

E=12LI2+12CV2E = \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=12LI2+12CV2E = \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=12LI2+12CV2E = \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=12LI2+12CV2E = \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=12LI2+12CV2E = \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.


Related Solutions

A capacitor is fully charged and then connected in series to an inductor with zero resistance...
A capacitor is fully charged and then connected in series to an inductor with zero resistance wires. This is an ideal L-C circuit that will oscillate the current direction. Explain HOW and WHY this circuit oscillates and discuss energy conservation in this oscillation behavior. Your response should be at least 3 paragraphs to show your mastery of the concepts.
A capacitor is fully charged and then connected in series to an inductor with zero resistance...
A capacitor is fully charged and then connected in series to an inductor with zero resistance wires. This is an ideal L-C circuit that will oscillate the current direction. Explain HOW and WHY this circuit oscillates and discuss energy conservation in this oscillation behavior. Your response should be at least 3 paragraphs to show your mastery of the concepts.
A capacitor is fully charged and then connected in series to an inductor with zero resistance...
A capacitor is fully charged and then connected in series to an inductor with zero resistance wires. This is an ideal L-C circuit that will oscillate the current direction. Explain HOW and WHY this circuit oscillates and discuss energy conservation in this oscillation behavior. Your response should be at least 3 paragraphs to show your mastery of the concepts.
10.An AC voltage source is connected in series to an inductor, a capacitor, and a resistor...
10.An AC voltage source is connected in series to an inductor, a capacitor, and a resistor of 8 Ohms. At the frequency when the phase angle is zero, capacitive reactance is 7 Ohms. What is the phase angle between the current and voltage at a frequency which is a factor of 3.2 times less than this frequency? answer in degresss and if negative 6. the resistance of a coil spun in a generator is 2 Ohms. the coil is in...
1- A charged capacitor and an inductor are connected at time t=0. After three and a...
1- A charged capacitor and an inductor are connected at time t=0. After three and a quarter periods of the resulting oscillations, which of the following quantities reaches its maximum? A. EMF on the inductor B. Magnetic energy C. magnetic flux through the inductor D. None of the above 2- A 1 H superconducting inductor in an oscillating LC circuit with angular frequency 1000 s-1 holds a maximum voltage on a capacitor 1000 V. The maximum current through the inductor...
A 159 ?H inductor is connected to a 159 pF capacitor to form an ideal series...
A 159 ?H inductor is connected to a 159 pF capacitor to form an ideal series resonance circuit and another ideal parallel resonance circuit. a) Find the resonance frequency for both circuits b) Find an expression for the impedance and the magnitude of the impedance for both circuits c) Sketch a rough plot of the impedance behavior with changing frequency
A resistor, inductor, and capacitor are connected in parallel with a function generator. Calculate the apparent...
A resistor, inductor, and capacitor are connected in parallel with a function generator. Calculate the apparent power of the circuit. Enter your answer in VA but do not enter the unit. Round to the nearest whole VA. VT = 117V RMS, R = 170Ω, XL = 169Ω, XC = 46Ω
Q4. A science project exhibit, a capacitor is connected in series with a bulb connected to...
Q4. A science project exhibit, a capacitor is connected in series with a bulb connected to an ac source. If its voltage amplitude is held constant, choose the correct option for the light bulb to glow the brightest at (a) high frequencies (b) low frequencies (c) The brightness will be same at all frequencies. At what frequency the light bulb will glow the dimmest, if capacitor is replaced by inductor? When an AC source is replaced by DC source find...
Q4. A science project exhibit, a capacitor is connected in series with a bulb connected to...
Q4. A science project exhibit, a capacitor is connected in series with a bulb connected to an ac source. If its voltage amplitude is held constant, choose the correct option for the light bulb to glow the brightest at (a) high frequencies (b) low frequencies (c) The brightness will be same at all frequencies. At what frequency the light bulb will glow the dimmest, if capacitor is replaced by inductor? When an AC source is replaced by DC source find...
A 24.0-V battery is connected in series with a resistor and an inductor, with R =...
A 24.0-V battery is connected in series with a resistor and an inductor, with R = 4.60 Ω and L = 7.00 H, respectively. (a) Find the energy stored in the inductor when the current reaches its maximum value. ________J (b) Find the energy stored in the inductor at an instant that is a time interval of one time constant after the switch is closed. ________J
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT