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Consider an RL circuit consisting of an inductor with an inductance of I henry (H) and a resistor with a resistance of R ohms () driven by a voltage of E(t) volts (V). Given the voltage drop across the resistor is ER = RI, and across the inductor is EL = L(dI / dt), Kirchhoff's Law gives dI L + RI = E(t) dt Now suppose an RL circuit with a 62 resistor and a 0.01H inductor is driven by a constant voltage E(t) sin (170t) V. If the initial resistor current is I(0) = 0A, find the current I and the voltages across the inductor E and the resistor ER in terms of time t. =

Consider an RL circuit consisting of an inductor with an inductance of I henry (H) and a resistor with a resistance of R ohms () driven by a voltage of E(t) volts (V). Given the voltage drop across the resistor is ER = RI, and across the inductor is EL = L(dI / dt), Kirchhoff's Law gives dI L + RI = E(t) dt Now suppose an RL circuit with a 62 resistor and a 0.01H inductor is driven by a constant voltage E(t) sin (170t) V. If the initial resistor current is I(0) = 0A, find the current I and the voltages across the inductor E and the resistor ER in terms of time 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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Consider an RL circuit consisting of an inductor with an inductance of L henry (H) and a resistor with a resistance of R ohms (1) driven by a voltage of E(t) volts (V). Given the voltage drop across the resistor is ER RI, and across the inductor is E₁ = L(dI / dt), Kirchhoff's Law gives EL I(t) = = ER(t) EL (t) = L = dI dt Now suppose an RL circuit with a 62 resistor and a 0.01H inductor is driven by a constant voltage E(t) = sin(170t)V. If the initial resistor current is I(0) = 0A, find the current I and the voltages across the inductor E and the resistor E in terms of time t. = + RI = E(t) A V V
Transcribed Image Text:Consider an RL circuit consisting of an inductor with an inductance of L henry (H) and a resistor with a resistance of R ohms (1) driven by a voltage of E(t) volts (V). Given the voltage drop across the resistor is ER RI, and across the inductor is E₁ = L(dI / dt), Kirchhoff's Law gives EL I(t) = = ER(t) EL (t) = L = dI dt Now suppose an RL circuit with a 62 resistor and a 0.01H inductor is driven by a constant voltage E(t) = sin(170t)V. If the initial resistor current is I(0) = 0A, find the current I and the voltages across the inductor E and the resistor E in terms of time t. = + RI = E(t) A V V
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Step 1: Introduction of the given problem

L fraction numerator d I over denominator d t end fraction plus R I equals E open parentheses t close parentheses I open parentheses 0 close parentheses equals 0 R equals 6 space capital omega L equals 0.01 space H E open parentheses t close parentheses equals sin open parentheses 170 t close parentheses space V

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