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A circuit is comprised of an induetor, a capacitor, a battery and a switch. When e switch is in position "a", the battery is in series with the capacitor, but the inductor is excluded. Vhen the switch is in position "b", the capacitor and the inductor are in series, but the battery is xeluded. Two voltmeters and an ammeter have been added to the circuit, as shown. 8% Part (a) Initially the switch is moved to position "a" where it remains until the capacitor attains its maximum charge. Enter an expression for the aximum charge on the capacitor. à & 8% Part (b) Once the capacitor is fully charged, the switch is moved from position "a" to position "b". Let q represent the charge on the capacitor, and tI represent the current measured by the ammeter at any given time after the switch is moved to position "b". Enter an expression for a Kirchhoff Loop Rule quation for the circuit that now includes both the capacitor and the inductor. a 8% Part (e) Current is the derivative of charge with respect to time. Use this information to eliminate current from your Kirchhoff Loop Rule equation. nter an expression for the second derivative of charge with respect to time. A S% Part (d) When the second derisratise of a function is proportional to the onposite of the original fnction then e kno from calculus and from

A circuit is comprised of an induetor, a capacitor, a battery and a switch. When e switch is in position "a", the battery is in series with the capacitor, but the inductor is excluded. Vhen the switch is in position "b", the capacitor and the inductor are in series, but the battery is xeluded. Two voltmeters and an ammeter have been added to the circuit, as shown. 8% Part (a) Initially the switch is moved to position "a" where it remains until the capacitor attains its maximum charge. Enter an expression for the aximum charge on the capacitor. à & 8% Part (b) Once the capacitor is fully charged, the switch is moved from position "a" to position "b". Let q represent the charge on the capacitor, and tI represent the current measured by the ammeter at any given time after the switch is moved to position "b". Enter an expression for a Kirchhoff Loop Rule quation for the circuit that now includes both the capacitor and the inductor. a 8% Part (e) Current is the derivative of charge with respect to time. Use this information to eliminate current from your Kirchhoff Loop Rule equation. nter an expression for the second derivative of charge with respect to time. A S% Part (d) When the second derisratise of a function is proportional to the onposite of the original fnction then e kno from calculus and from

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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A circuit is comprised of an inductor, a capacitor, a battery and a switch. When a he switch is in position "a", the battery is in series with the capacitor, but the inductor is excluded. When the switch is in position "b", the capacitor and the inductor are in series, but the battery is excluded. Two voltmeters and an ammeter have been added to the circuit, as shown. Vc VL Vo > A 8% Part (a) Initially the switch is moved to position "a" where it remains until the capacitor attains its maximum charge. Enter an expression for the maximum charge on the capacitor. Inax = - A 8% Part (b) Once the capacitor is fully charged, the switch is moved from position "a" to position "b". Let q represent the charge on the capacitor, and et I represent the current measured by the ammeter at any given time after the switch is moved to position "b". Enter an expression for a Kirchhoff Loop Rule quation for the circuit that now includes both the capacitor and the inductor. -A 8% Part (c) Current is the derivative of charge with respect to time. Use this information to eliminate current from your Kirchhoff Loop Rule equation. Enter an expression for the second derivative of charge with respect to time. - A 8% Part (d) When the second derivative of a function is proportional to the opposite of the original function, then we know from calculus and from imple harmonic motion that the solution may be represented with a sine or a cosine function. If we write the solution as q(t) = nitial conditions at the instant the switch is moved to position "b", and enter an expression for the phase constant, o. -A 8% Part (e) If we write the solution as q(t) = A cos(wt + 4), consider the initial conditions at the instant the switch is moved to position "b", and enter an expression for the amplitude, A. A cos(wt + o), consider the d?q in order to dt? - A 8% Part (f) Take appropriate derivatives of q(t) A cos(wt + 4) and substitute them into the equation that you previously entered for liscover an expression for w. Enter that expression. - A 8% Part (g) Enter an expression for the voltage across the capacitor as a function of time as measured by the voltmeter labeled Vc. -A 8% Part (h) Enter an expression for the voltage across the inductor as a function of time as measured by the voltmeter labeled VL. - A 8% Part (i) Enter an expression for the sum of the voltages across the inductor and the capacitor. -A 8% Part ((j) Enter an expression for the energy stored by the capacitor as a function of time. -A 8% Part (k) Enter an expression for the energy stored by the inductor as a function of time. -A 8% Part (1) Enter an expression for the sum of the energies stored by the capacitor and the inductor as a function of time. - A 8% Part (m) Which statement best describes the energy flow in the circuit while the switch is in position "b"?
Transcribed Image Text:A circuit is comprised of an inductor, a capacitor, a battery and a switch. When a he switch is in position "a", the battery is in series with the capacitor, but the inductor is excluded. When the switch is in position "b", the capacitor and the inductor are in series, but the battery is excluded. Two voltmeters and an ammeter have been added to the circuit, as shown. Vc VL Vo > A 8% Part (a) Initially the switch is moved to position "a" where it remains until the capacitor attains its maximum charge. Enter an expression for the maximum charge on the capacitor. Inax = - A 8% Part (b) Once the capacitor is fully charged, the switch is moved from position "a" to position "b". Let q represent the charge on the capacitor, and et I represent the current measured by the ammeter at any given time after the switch is moved to position "b". Enter an expression for a Kirchhoff Loop Rule quation for the circuit that now includes both the capacitor and the inductor. -A 8% Part (c) Current is the derivative of charge with respect to time. Use this information to eliminate current from your Kirchhoff Loop Rule equation. Enter an expression for the second derivative of charge with respect to time. - A 8% Part (d) When the second derivative of a function is proportional to the opposite of the original function, then we know from calculus and from imple harmonic motion that the solution may be represented with a sine or a cosine function. If we write the solution as q(t) = nitial conditions at the instant the switch is moved to position "b", and enter an expression for the phase constant, o. -A 8% Part (e) If we write the solution as q(t) = A cos(wt + 4), consider the initial conditions at the instant the switch is moved to position "b", and enter an expression for the amplitude, A. A cos(wt + o), consider the d?q in order to dt? - A 8% Part (f) Take appropriate derivatives of q(t) A cos(wt + 4) and substitute them into the equation that you previously entered for liscover an expression for w. Enter that expression. - A 8% Part (g) Enter an expression for the voltage across the capacitor as a function of time as measured by the voltmeter labeled Vc. -A 8% Part (h) Enter an expression for the voltage across the inductor as a function of time as measured by the voltmeter labeled VL. - A 8% Part (i) Enter an expression for the sum of the voltages across the inductor and the capacitor. -A 8% Part ((j) Enter an expression for the energy stored by the capacitor as a function of time. -A 8% Part (k) Enter an expression for the energy stored by the inductor as a function of time. -A 8% Part (1) Enter an expression for the sum of the energies stored by the capacitor and the inductor as a function of time. - A 8% Part (m) Which statement best describes the energy flow in the circuit while the switch is in position "b"?
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