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 I(t) = Now suppose an RL circuit with a 72 resistor and a 0.04H inductor is driven by a constant voltage E(t) = sin(40t)V. If the initial resistor current is I(0) = 0A, find the current I and the voltages across the inductor E₁ and the resistor ER in terms of time t = ER(t) EL(t) = = dI L + RI = E(t) dt A V V
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 I(t) = Now suppose an RL circuit with a 72 resistor and a 0.04H inductor is driven by a constant voltage E(t) = sin(40t)V. If the initial resistor current is I(0) = 0A, find the current I and the voltages across the inductor E₁ and the resistor ER in terms of time t = ER(t) EL(t) = = dI L + RI = E(t) dt A V V
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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Question
Consider an RL circuit consisting of an inductor with an inductance of L henry (H) and a resistor with a resistance of R ohms (Ω)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 Ld Idt+RI =E(t)
Now suppose an RL circuit with a 7Ω resistor and a 0.04H inductor is driven by a constant voltage of sin(40t) V. If the initial resistor current is I(0)=0A , find the current I and the voltages across the inductor EL and the resistor ER in terms of time t.
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 Rohms (22) 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
I(t)
Now suppose an RL circuit with a 7º resistor and a 0.04H inductor is driven by a
constant voltage E(t) = sin(40t)V. If the initial resistor current is I(0) = 0A, find the
current I and the voltages across the inductor EL and the resistor ER in terms of time t
=
ER(t)
EL(t)
=
-
=
dI
L- + RI = E(t)
dt
A
V
V
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