When a voltage V is applied to a series circuit consisting of a resistor R and an inductor L, the current at time t is I(1) = )(1 G (1-e-RilL) e-RUIL) Expand I(t) to its Maclaurin series. Choose the Maclaurin series. V (-1)*+1 ( Rt I(t) R n=1 n! V I(t) (-1)" (#)' Rt \" (п + n=1 (-1)*+1 n V L I(t) Σ n! Rt n=1 n+1 V I(t) (-1)" L п! Rt n=1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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When a voltage V is applied to a series circuit consisting of a resistor R and an inductor L, the current at time t is
I(1) = ) (1 - e-RIL)
Expand I(t) to its Maclaurin series.
Choose the Maclaurin series.
00
V
(-1)"+1 ( Rt \n
I(t)
Σ
R
n=1
п!
L
00
(-1)"
(п + 1)!
V
Rt
Σ
I(t)
R
n=1
00
n
V
(-1y*+1
L
I(t)
R
n=1
n!
Rt
00
n+1
V
(-1)" ( L
I(t)
R
n=1
п!
Rt
Transcribed Image Text:When a voltage V is applied to a series circuit consisting of a resistor R and an inductor L, the current at time t is I(1) = ) (1 - e-RIL) Expand I(t) to its Maclaurin series. Choose the Maclaurin series. 00 V (-1)"+1 ( Rt \n I(t) Σ R n=1 п! L 00 (-1)" (п + 1)! V Rt Σ I(t) R n=1 00 n V (-1y*+1 L I(t) R n=1 n! Rt 00 n+1 V (-1)" ( L I(t) R n=1 п! Rt
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