In the circuit shown in Figure, a generator supplies a voltage of volts, the inductance is 2 H, the resistance is 40 , and . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.

Question

In the circuit shown in Figure, a generator supplies a voltage of  volts, the inductance is 2 H, the resistance is 40  , and  . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.

Quizplus · Accepted Answer

Using Kirchhoff's voltage law (KVL), we have:

$V_g - IR - L\frac{dI}{dt} = 0$

Taking the derivative of both sides and plugging in values, we get:

$\frac{d^2I}{dt^2} + \frac{1}{5}\frac{dI}{dt} + \frac{11}{100}I = 0$

Solving for $I$, we get:

$I(t) = e^{-\frac{t}{10}}\left(A\cos\left(\frac{\sqrt{39}}{10}tight) + B\sin\left(\frac{\sqrt{39}}{10}tight)ight)$

Using the initial condition $I(0) = 0$, we get:

$I(t) = \frac{11}{\sqrt{39}}\left(1 - e^{-\frac{t}{10}}ight)\sin\left(\frac{\sqrt{39}}{10}tight)$

Plugging in $t = 0.2$, we get:

$I(0.2) \approx \boxed{0.70 	ext{ or } 0.71 	ext{ (rounded to two decimal places)}}$

In the Circuit Shown in Figure, a Generator Supplies a Voltage