Consider the parallel inductors shown in Figure P3.67, with mutual coupling and the dots at the top ends of L 1 and L 2 . Derive an expression for the equivalent inductance seen by the source in terms of L 1 , L 2 , and M . [Hint: Write the circuit equations and manipulate them to obtain an expression of the form v ( t ) = L e q d i ( t ) / d t in which L e q is a function of L 1 , L 2 , and M .]
Consider the parallel inductors shown in Figure P3.67, with mutual coupling and the dots at the top ends of L 1 and L 2 . Derive an expression for the equivalent inductance seen by the source in terms of L 1 , L 2 , and M . [Hint: Write the circuit equations and manipulate them to obtain an expression of the form v ( t ) = L e q d i ( t ) / d t in which L e q is a function of L 1 , L 2 , and M .]
Consider the parallel inductors shown in Figure P3.67, with mutual coupling and the dots at the top ends of
L
1
and
L
2
. Derive an expression for the equivalent inductance seen by the source in terms of
L
1
,
L
2
, and M. [Hint: Write the circuit equations and manipulate them to obtain an expression of the form
v
(
t
)
=
L
e
q
d
i
(
t
)
/
d
t
in which
L
e
q
is a function of
L
1
,
L
2
, and M.]
In the Figure Q3(c), determine the value of R for which the steady-state energy storedin the inductor will be 0.25J.
Two initially uncharged capacitors C 1 = 15 μF and C 2 =10 μF are connected in series. Then, a 10-V source is connected to the series combination, as shown in Figure P3.28. Find the voltages v1 and v2 after the source is applied. [Hint: The charges stored on the two capacitors must be equal, because the current is the same for both capacitors.]
A 10-mH inductor has a parasitic series resistance of R s =1 Ω, as shown in FigureP3.68.a. The current is given by i( t )=0.1 cos( 10 5 t ). Find v R ( t ), v L ( t ), and v(t). In thiscase, for 1-percent accuracy in computing v(t), could the resistance be neglected?b. Repeat if i( t )=0.1 cos( 10t ).
Chapter 3 Solutions
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Inductors Explained - The basics how inductors work working principle; Author: The Engineering Mindset;https://www.youtube.com/watch?v=KSylo01n5FY;License: Standard Youtube License