IP Suppose the resistor in the figure has the value 16 ? and that the switch is

Question

IP Suppose the resistor in the figure has the value 16 ? and that the switch is closed at time t=0. (Figure 1)

Part A

How much energy is stored in the inductor at the time t=??

Express your answer using two significant figures. *The answer should be in J

Part B

How much energy is stored in the inductor at the time t=2??

Express your answer using two significant figures.*The answer should be in J

Part C

If the value of R is increased, does the characteristic time, ?, increase or decrease?

Explanation / Answer

Overall resistance R = 16 in parallel with 7 = 4.87

If the current is initially zero in an LR circuit, its value at some later time t is given by

I = Io*[1-e^-t/]

where If = 0/R = 2.464 A

and = L/R = 0.0127 s is the time constant for the circuit. We can find the time at which the power dissipation in the resistor equals the rate at which magnetic energy is stored in the inductor

At t =

Energy stored in the inductor = 1/2*Li^2 = 1/2*L*Io^2[1-e^-t/]^2 = 1/2*63*10^-3*2.464^2[1-e^-1]^2 = 0.12 J

At t = 2

Energy stored in the inductor = 1/2*Li^2 = 1/2*L*Io^2[1-e^-t/]^2 = 1/2*63*10^-3*2.464^2[1-e^-2]^2 = 0.165 J

If R is increased the = L/R will decrease.

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