The current in a 50 mH inductor is known to be i=120\

Question

The current in a 50 mH inductor is known to be i=120\

diferira7c 2022-01-17 Answered

The current in a 50 mH inductor is known to be

i = 120 m A, t \leq 0; i = A_{1} e^{- 500 t} + A_{2} e^{- 2000 t} A, t \geq 0

The voltage across the inductor (passive sign convention) is 3 V at t =0. a) Find the expression for the voltage across the inductor for t > 0. b) Find the time, greater than zero, when the power at the terminals of the inductor is zero.

Ask Expert 3 See Answers

You can still ask an expert for help

Answers (3)

godsrvnt0706

Answered 2022-01-19 Author has 31 answers

b)

p = v i

so we search for when the voltage of the current are zero:

i (t) = 0.2 e^{- 500 t} - 0.08 e^{- 2000 t}

i (t) = 0 \Rightarrow

0.2 e^{- 500 t} = \frac{0}{08} e^{- 2000 t}

\frac{0.2}{0.08} = \frac{e^{- 2000 t}}{e^{- 500 t}}

\ln (2.5) = \ln (e^{- 1500 t}

t = \frac{- \ln (2.5)}{1500}

t = - 6.1 \cdot 10^{- 4} s

PSKWhich is not greater than zero. Lets

This is helpful 0

RizerMix

Answered 2022-01-19 Author has 438 answers

a) We know that $i (0) = 120$ mA so we can write
$i (0) = A_{1} e^{0} + A_{2} e^{0} = A_{1} + A_{2} = 0.12 A$
We also kno that $v (0) = 3 V$ so we write
$\frac{d i}{d t} = - 500 A_{1} e^{- 500 t} - 2000 A_{2} e^{- 2000 t} v = L \frac{d i}{d t} = - 25 A_{1} e^{- 500 t} - 100 A_{2} e^{- 2000 t} v (0) = - 25 A_{1} e^{0} - 100 A_{2} e^{0} = - 25 A_{1} - 100 A_{2} = 3 V v (0) = 25 A_{1} e^{0} - 100 A_{2} e^{0} = - 25 A_{1} - 100 A_{2} = 3 V$
Now we have two equations with two unknowns:
$A_{1} + A_{2} = 0.12 - 25 A_{1} - 100 A_{2} = 3$
We solve this and get
$A_{1} = 0.2 a n d A_{2} = - 0.08$
Now we can write the expression for the voltage
$v (t) = - 25 (0.2) e^{- 500 t} - 100 (- 0.08) e^{- 2000 t} v (t) = - 5 e^{- 500 t} + 8 e^{- 2000 t} V$

This is helpful 0

alenahelenash

Answered 2022-01-23 Author has 343 answers

You help me, thanks!

This is helpful 0

Relevant Questions

asked 2021-02-20

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Fig. 1) The rope will break if the tension in it exceeds $4.50 \cdot 10^{4}$ N and our hero's mass is 86.5 kg.

Figure 1 a) If the angle $θ$ is ${13.0}^{\circ}$ , find the tension iin the rope.

b) What is the smallest value the angle $θ$ can have if the rope is not to break?

See answers (1)

asked 2021-01-08

A 500 g ball swings in a vertical circle at the end of a1.5-m-long string. When the ball is at the bottom of the circle,the tension in the string is 15 N.
What is the speed of the ball at that point?

See answers (1)

asked 2020-11-23

Saturn has an equatorial radius of 6.00 107 mand a mass of 5.67 1026 kg.
(a) Compute the acceleration of gravity at the equatorof Saturn.
(b) What it the ratio of a person's weight on Saturn to that onEarth?

See answers (1)

asked 2020-11-01

A horizontal force of 210N is exerted on a 2.0 kg discus as it rotates uniformaly in a horizontal circle ( at arm's length ) of radius .90 m. Calculate the speed of the discus

See answers (1)