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. =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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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 (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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2323f944-68c6-4ffb-b4bd-7709a3866c17%2F4ba203f0-ad63-4e5b-8e54-a6dcc94bfd27%2Flc157vj_processed.png&w=3840&q=75)
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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