For this problem and the next, use the following information. A switch, an induc

Question

For this problem and the next, use the following information. A switch, an inductor and a 68.0 Ohm resistor are connected in series across an ideal battery z - 9 0 V The switch is inrtialy open A The switch is now suddenly closed at time t = 0 and in 25.0 micro-seconds the current in the circuit reaches a value of 95 0 mA What is the value of the inductor? Give your answer in the form "a bc times 10^(y)"H B How much energy is stored in the inductor at this time7 Give your answer in the form "a bc times 10 ^ (y) Joule

Explanation / Answer

series RL circuit

time constant T= L/R = L/68

A) charging current of the circuit

i(t) = Imax*(1 - e^(-t/T))

where Imax = E/68 = 9/68 =0.132 A

at t = 25*10^-6 sec , i(t)= 95.0 mA

=> 95.0*10^-3 = 0.132*(1 - e^(-t/T))

=> 0.719 = 1 - e^(-t/T)

=> e^(-t/T) = 0.281

=> t/T = 1.26 => T = t/1.26 = 25*10^-6/1.26 = 19.84*10^-6

=> L = 19.84*10^-6*68 = 1.349*10^-3 H

B) energy stored E = (L*i^2)/2 = 1.349*10^-3*(95*10^-3)^2/2 = 6.087*10^-6 joule

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