Chapter 5.3, Problem 114AYU

a.

To determine

To find:

(a) If $E=120$ volts, $R=2000$ ohms and $C=1.0$ microfarads, how much current $I_1$ is flowing initially $t=0$ ? After 1000 microseconds? After 3000 microseconds?

Answer to Problem 114AYU

Solution:

(a) $0.06A$ current $I_1$ is flowing initially $t=0$ , $$ E=120$0.0364 A$ current $I_1$ is flowing after $1000$ microseconds, $0.0134 A$ current $I_1$ is flowing after $3000$ microseconds.

Explanation of Solution

Given:

  $I= \frac{E}{R}\left[e^{-\frac{t}{RC}}\right]$

  $$ $ 0.06A$I_1$ t=0$$I_1$$1000$$0.0134 A$

Calculation:

  

b.

To determine

To find:

(b) The maximum current.

Answer to Problem 114AYU

Solution:

(b) $0.06A$ maximum current when time approaches zero.

Explanation of Solution

Given:

  $I= \frac{E}{R}\left[e^{-\frac{t}{RC}}\right]$

Calculation:

(b) We obtain maximum current when time approaches zero

  $= \frac{120}{2000}\left[e^{-\frac{0}{2000\left(1\right)}}\right]$

  $= \frac{12}{200}\left[1\right]$

  $= 0.06A$

c.

To determine

To find:

(c) graph the function $I= I_1\left(t\right),$ measuring $I$ along the y -axis and t along the x -axis.

Answer to Problem 114AYU

Solution:

(c)

  

Explanation of Solution

Given:

  $I= \frac{E}{R}\left[e^{-\frac{t}{RC}}\right]$

Calculation:

(c)

  

d.

To determine

To find:

(d) If $E=120$ volts, $R=1000$ ohms, and $C=2.0$ microfarads, how much current $I_1$ is flowing initially $t=0$ ? After 1000 microseconds? After 3000 microseconds?

Answer to Problem 114AYU

Solution:

(d) $0.12 A$ current $I_1$ is flowing initially $t=0$ , $0.0727 A$ current $I_1$ is flowing after $1000$ microseconds, $0.0268 A$ current $I_1$ is flowing after $3000$ microseconds.

Explanation of Solution

Given:

  $I= \frac{E}{R}\left[e^{-\frac{t}{RC}}\right]$

Calculation:

  

e.

To determine

To find:

(e) The maximum current.

Answer to Problem 114AYU

Solution:

(e) $0.12A$ maximum current when time approaches zero.

Explanation of Solution

Given:

  $I= \frac{E}{R}\left[e^{-\frac{t}{RC}}\right]$

Calculation:

(e) We obtain maximum current when time approaches zero

  $= \frac{120}{1000}\left[e^{-\frac{0}{2000\left(1\right)}}\right]$

  $= \frac{12}{100}\left[1\right]$

  $= 0.12A$

f.

To determine

To find:

(f) graph the function $I= I_2\left(t\right),$ measuring $I$ along the y -axis and t along the x -axis.

Answer to Problem 114AYU

Solution:

(f)

  

Explanation of Solution

Given:

  $I= \frac{E}{R}\left[e^{-\frac{t}{RC}}\right]$

Calculation:

(f)