Question

Consider an L-R circuit as shown in the figure. (Figure 1) The battery provides 12.0V of voltage. The inductor has inductance L, and the resistor has resistance R = 150? . The switch is initially open as shown. At time t=0, the switch is closed. At time tafter t=0 the current I(t) flows through the circuit as indicated in the figure.

Part C

What is the current reading I(?) given by the ammeter shown in the circuit (Figure 4) at one time constant after t=0?

Express your answer in amperes.

Answer 1

To find the current in the circuit after one time constant,use the expressionfor I(t)= V/R(1-e^-t/?) with tequal to

After plugging in the numerical values for Vand R appropriate for this circuit andsubstituting ? for time, simplify your expression to geta numerical value for the current.

So I substitued ? for t and got:

                                          I(?)= V/R(1-e^-?/?)

which simplifies to:

                                          I(?)= V/R(1-e^-1)

Then plug in your values for V and R:

                                          I(?)= 12/150(1-e^-1)

Simplify and get:

                                          I(?)=5.06 x 10^-2 A