Chapter 5.3, Problem 121AYU

119. Current in an RL Circuit The equation governing the amount of current I (in amperes) after time t (in seconds) in a single RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys), and an electromotive force E (in voles) is

$I = \frac{E}{R}[1 - e^{-(R/L)t}]$

(a) If $E = 120$ volts, $R = 10$ ohms, and $L = 5$henrys, how much current I₁ is flowing after 0.3 second? After 0.5 second? After 1 second?

(b) What is the maximum current?

(c) Graph this function $I = I_1$ (t), measuring I along the $y\text{-axis}$ and t along the $x\text{-axis}$.

(d) If $E = 120$ volts, $R=5$ ohms, and $L = 10$ henrys, how much current I₂ is flowing after 0.3 second? After 0.5 second? After 1 second?

(e) What is the maximum current?

(f) Graph the function $I = I_2\left(t\right)$ on the same coordinate axes as $I_1(t)$.