In an electric Circuit , total energy Cin Joules)dissipated elements between t, =0byby E,and tz= 20 msis given -I(t) * V (+) dt. If the current,-100ICt) = (25)ein mA and the voltage ,V(t) = 15 -5et00in V,%3DFind the tatalL energy dissipated,

Given, Vt=15-5e-100t VI(t)=25e-100t mAt1=0 st2=20 msE=∫t1t2It×Vt dt

Answered: In an electric Circuit , total energy…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Question

In an electric Circuit , total energy Cin Joules)
dissipated elements between t, =0
by
by E
,and tz= 20 ms
is given -
I(t) * V (+) dt. If the current,
-100
ICt) = (25)e
in mA and the voltage ,V(t) = 15 -5et00
in V,
%3D
Find the tatalL energy dissipated,

Expert Solution

Step 1

Given,

$V (t) = 15 - 5 e^{- 100 t} V I (t) = 25 e^{- 100 t} m A t_{1} = 0 s t_{2} = 20 m s E = \int_{t_{1}}^{t_{2}} I (t) \times V (t) d t$

Step 2

$E = \int_{t_{1}}^{t_{2}} I (t) \times V (t) d t E = \int_{t_{1}}^{t_{2}} 25 e^{- 100 t} \times 10^{- 3} \times (15 - 5 e^{- 100 t}) d t E = 25 \times 10^{- 3} \int_{t_{1}}^{t_{2}} e^{- 100 t} \times (15 - 5 e^{- 100 t}) d t E = 25 \times 10^{- 3} \int_{t_{1}}^{t_{2}} 15 e^{- 100 t} - 5 e^{- 200 t} d t E = 25 \times 10^{- 3} (15 {[\frac{e^{- 100 t}}{- 100}]}_{t_{1}}^{t_{2}} - 5 {[\frac{e^{- 200 t}}{- 200}]}_{t_{1}}^{t_{2}}) E = 25 \times 10^{- 3} (15 {[\frac{e^{- 100 t}}{- 100}]}_{0}^{20 m s} - 5 {[\frac{e^{- 200 t}}{- 200}]}_{0}^{20 m s}) E = 25 \times 10^{- 3} (15 [\frac{1 - e^{- 100 \times 20 \times 10^{- 3}}}{100}] - 5 [\frac{1 - e^{- 200 \times 20 \times 10^{- 3}}}{200}]) E = 25 \times 10^{- 3} (15 [\frac{0.864}{100}] - 5 [\frac{0.981}{200}]) E = 25 \times 10^{- 3} (0.1296 - 0.0245) E = 25 \times 10^{- 3} (0.1051) E = 2.6275 \times 10^{- 3} J E = 2.6275 m J$