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In the circuit above, we have a capacitor with capacitance 1 F, an inductor of inductance 3 H and a resistor of 22 (a) The total energy that is supplied to the resistor is LI Q? E = + 2 20 where L is the inductance, I is the current, C is the capacitance and Q is the charge. Write down the total energy supplied E in terms of Q and t only. Remember that I = ÒP dt (b) Now you know that the power dissipation through a resistor is -rR. Use the conservation of energy (energy gain rate = energy loss rate) to derive the differential equation in terms Q and t only. (c) Solve the differential equation for initial charge to be 0C with a initial V29 current of - 3 /s, where q is some constant amount of charge measured in Coulombs. (d) Given that the coefficient of your sine function is the time-dependent amplitude (for example A(t) is the amplitude of the function A(t) sin t). At what time T will the amplitude of the charge oscillations in the circiuitivatr be 75% of its initial value? Set

In the circuit above, we have a capacitor with capacitance 1 F, an inductor of inductance 3 H and a resistor of 22 (a) The total energy that is supplied to the resistor is LI Q? E = + 2 20 where L is the inductance, I is the current, C is the capacitance and Q is the charge. Write down the total energy supplied E in terms of Q and t only. Remember that I = ÒP dt (b) Now you know that the power dissipation through a resistor is -rR. Use the conservation of energy (energy gain rate = energy loss rate) to derive the differential equation in terms Q and t only. (c) Solve the differential equation for initial charge to be 0C with a initial V29 current of - 3 /s, where q is some constant amount of charge measured in Coulombs. (d) Given that the coefficient of your sine function is the time-dependent amplitude (for example A(t) is the amplitude of the function A(t) sin t). At what time T will the amplitude of the charge oscillations in the circiuitivatr be 75% of its initial value? Set

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help, Dont change subj, its a math problem
3. You have seen how Kirchhoff's laws were used in your lectures to obtain a 2nd order differential equation where we solved for the current. This time we will use an even simpler concept: principle of conservation of energy to derive the 2nd order differential equation where we will solve for the charge. Take a look at the circuit below. 1F ll
Transcribed Image Text:3. You have seen how Kirchhoff's laws were used in your lectures to obtain a 2nd order differential equation where we solved for the current. This time we will use an even simpler concept: principle of conservation of energy to derive the 2nd order differential equation where we will solve for the charge. Take a look at the circuit below. 1F ll
In the circuit above, we have a capacitor with capacitance 1 F, an inductor of inductance 3 H and a resistor of 22 (a) The total energy that is supplied to the resistor is LI Q? E = 2 2C where L is the inductance, I is the current, C is the capacitance and Q is the charge. Write down the total energy supplied E in terms of Q and t only. ÒP Remember that I = - dt (b) Now you know that the power dissipation through a resistor is -rR. Use the conservation of energy (energy gain rate = energy loss rate) to derive the differential equation in terms Q and t only. (c) Solve the differential equation for initial charge to be 0C with a initial /s, where q is some constant amount of charge measured 3 current of in Coulombs. (d) Given that the coefficient of your sine function is the time-dependent amplitude (for example A(t) is the amplitude of the function A(t) sin t). At what time T will the amplitude of the charge oscillations in the circnitivatr be 75% of its initial value? Set
Transcribed Image Text:In the circuit above, we have a capacitor with capacitance 1 F, an inductor of inductance 3 H and a resistor of 22 (a) The total energy that is supplied to the resistor is LI Q? E = 2 2C where L is the inductance, I is the current, C is the capacitance and Q is the charge. Write down the total energy supplied E in terms of Q and t only. ÒP Remember that I = - dt (b) Now you know that the power dissipation through a resistor is -rR. Use the conservation of energy (energy gain rate = energy loss rate) to derive the differential equation in terms Q and t only. (c) Solve the differential equation for initial charge to be 0C with a initial /s, where q is some constant amount of charge measured 3 current of in Coulombs. (d) Given that the coefficient of your sine function is the time-dependent amplitude (for example A(t) is the amplitude of the function A(t) sin t). At what time T will the amplitude of the charge oscillations in the circnitivatr be 75% of its initial value? Set
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