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If we differentiate this equation with respect to time and substitute I = dq dt a second-order differential equation L d²I dt² dI 1 + R + dt 7 Problem: Now suppose an RLC circuit with a 25 100 F capacitor is driven by the voltage E(t) 27 T1, T2 = = I= dE dt resistor, a 0.09t² V. 1 100 we obtain H inductor, and a d² I dI i. Using differential operator notation, dt² dt differential equation associated with this circuit in terms of current I, differential operator D, and time t. = D²I and = DI, write the ii. Find the roots of the auxiliary polynomial of the corresponding homogeneous equation of I. Enter the roots as a list separated by commas. iii. Find the general solution of the corresponding homogeneous equation (complementary solution) for I. Use A and B for the arbitrary constants. Ih(t) iv. Find a particular solution for I. Where needed, round off all your values to at least five decimal places. Ip(t) v. Find the general solution for I in terms of t and arbitrary contastands A and B. I(t) =

If we differentiate this equation with respect to time and substitute I = dq dt a second-order differential equation L d²I dt² dI 1 + R + dt 7 Problem: Now suppose an RLC circuit with a 25 100 F capacitor is driven by the voltage E(t) 27 T1, T2 = = I= dE dt resistor, a 0.09t² V. 1 100 we obtain H inductor, and a d² I dI i. Using differential operator notation, dt² dt differential equation associated with this circuit in terms of current I, differential operator D, and time t. = D²I and = DI, write the ii. Find the roots of the auxiliary polynomial of the corresponding homogeneous equation of I. Enter the roots as a list separated by commas. iii. Find the general solution of the corresponding homogeneous equation (complementary solution) for I. Use A and B for the arbitrary constants. Ih(t) iv. Find a particular solution for I. Where needed, round off all your values to at least five decimal places. Ip(t) v. Find the general solution for I in terms of t and arbitrary contastands A and B. I(t) =

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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Theory: Consider an RLC circuit shown below consisting of an inductor with an inductance of I henry (H), a resistor with a resistance of R ohms (2), and a capacitor with a capacitance of C farads (F) driven by a voltage of E(t) volts (V). = Given the voltage drop across the resistor is ER = RI, across the inductor is L(dI / dt), and across the capacitor is Ec 9 EL Kirchhoff's Law gives C E| L T1, T2 = dI dt L In(t) R If we differentiate this equation with respect to time and substitute I = dq dt a second-order differential equation = с d²I dt² = 1 + RI + 69 7 Problem: Now suppose an RLC circuit with a 25 dI + R + dt = 1 E(t) с -I = 100 -F capacitor is driven by the voltage E(t) = 0.09t² V. 27 dE dt resistor, a d²I dI i. Using differential operator notation, dt² dt differential equation associated with this circuit in terms of current I, differential operator D, and time t. D²I and 1 100 ii. Find the roots of the auxiliary polynomial of the corresponding homogeneous equation of I. Enter the roots as a list separated by commas. we obtain H inductor, and a iii. Find the general solution of the corresponding homogeneous equation (complementary solution) for I. Use A and B for the arbitrary constants. = DI, write the iv. Find a particular solution for I. Where needed, round off all your values to at least five decimal places. Ip(t) v. Find the general solution for I in terms of t and arbitrary contastands A and B. I(t)
Transcribed Image Text:Theory: Consider an RLC circuit shown below consisting of an inductor with an inductance of I henry (H), a resistor with a resistance of R ohms (2), and a capacitor with a capacitance of C farads (F) driven by a voltage of E(t) volts (V). = Given the voltage drop across the resistor is ER = RI, across the inductor is L(dI / dt), and across the capacitor is Ec 9 EL Kirchhoff's Law gives C E| L T1, T2 = dI dt L In(t) R If we differentiate this equation with respect to time and substitute I = dq dt a second-order differential equation = с d²I dt² = 1 + RI + 69 7 Problem: Now suppose an RLC circuit with a 25 dI + R + dt = 1 E(t) с -I = 100 -F capacitor is driven by the voltage E(t) = 0.09t² V. 27 dE dt resistor, a d²I dI i. Using differential operator notation, dt² dt differential equation associated with this circuit in terms of current I, differential operator D, and time t. D²I and 1 100 ii. Find the roots of the auxiliary polynomial of the corresponding homogeneous equation of I. Enter the roots as a list separated by commas. we obtain H inductor, and a iii. Find the general solution of the corresponding homogeneous equation (complementary solution) for I. Use A and B for the arbitrary constants. = DI, write the iv. Find a particular solution for I. Where needed, round off all your values to at least five decimal places. Ip(t) v. Find the general solution for I in terms of t and arbitrary contastands A and B. I(t)
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