Please solve these both qustions!? Consider the circuit shown in the figure belo

Question

Please solve these both qustions!? Consider the circuit shown in the figure below where L = 5.30 mH and R_2 = 425 Ohm. (a) When the switch is in position a, for what value of R_1 will the circuit have a time constant of 14.5 mu S? k Ohm (b) What is the current in the inductor at the instant the switch is thrown to position b? mA A 140-mH inductor and a 4.80-Ohm resistor are connected with a switch to a 6.00-V battery as shown in the figure below. (a) After the switch is first thrown to a (connecting the battery), what time interval elapses before the current reaches 220 mA? ms (b) What is the current in the inductor 10.0 s after the switch is closed? A (c) Now the switch is quickly thrown from a to b. What time interval elapses before the current in the inductor falls to 160 mA? ms

Explanation / Answer

(a)

time constant T = L/R

R = (R1*R2)/(R1+R2)

T = L/R

14.5*10^-6 = 5.3*10^-3/R

R = 366

366 = (R1*425)/(R1+425)

R1 = 2636 ohms

R1 = 2.64 k ohm

(b)

I = (E/R)

I = (24/366)

I = 0.066 A

====================================

current increases as

i = (e/R)*(1-e^-(Rt/L))

0.220 = (6/4.8)*(1-e^-(4.8*t/0.14))

t = 5.64 ms

(b)

i = (6/4.8)*(1-e^-(4.8*10/0.14))

i = 1.25 A

(c)

current decreases as

i = (e/R)*e^-(Rt/L)

0.16 = (6/4.8)*e^-(4.8*t/0.14)

t = 60 ms

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