Q1 A 100 Volt battery and 5 micro-henry inductor are wired together in a series

Question

Q1

A 100 Volt battery and 5 micro-henry inductor are wired together in a series with a 100 ohm resistor and a switch forming a complete loop when the switch is closed. determine how long after the switch is close will the current through the inductor be .01 amp.

Q2
The 1000 turn secondary coil of an ideal transformer is connected to a 10 ohm resistor. determine the rms current in the 100 turn primary side if the rms current in the secondary side is .01 ( the trasnformer has almost no resistance.)

Explanation / Answer

1)

current through the circuit at time t is given by :

I = Io*(1-e^(-t/T))

where ,

Io = final current after at long time(when the inductor is short circuited)

So, Io = V/R = 100/100 = 1 A

T = time constant for the circuit = L/R = 5 micro / 100 = 5*10^-6/100 = 5*10^-8 s

So, for I = 0.01 A,

0.01 = 1*(1-e^(-t/(5*10^-8)))

So, t = 5.03*10^-10 s <-------------answer

2)

for a transformer,

primary to secondary voltage ratio = 100/1000

So, primary to secondary current ratio = 1000/100 = 10

So, current in primary side = 10*current in seconday = 10*0.01 = 0.1 A <------------answer

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