Consider a 25.0 mH inductor that has a resistance of 4.00 ohms. A. What is the c

Question

Consider a 25.0 mH inductor that has a resistance of 4.00 ohms. A. What is the characteristic time constant for the inductor? B. If it is connected to a 12.0V battery, what is the current after 12.5ms? C. If the inductor is connected to a 2.00 ohm in series and then connected to a 12.0V, what is the current after 12.5ms? D. If the inductor is connected to a 2.00 ohm in parallel and then connected to a 12.0V, what is the current after 12.5ms? E. What is the maximum current that will run through the inductor if it is connected to a 12.0V battery? Consider a 25.0 mH inductor that has a resistance of 4.00 ohms. A. What is the characteristic time constant for the inductor? B. If it is connected to a 12.0V battery, what is the current after 12.5ms? C. If the inductor is connected to a 2.00 ohm in series and then connected to a 12.0V, what is the current after 12.5ms? D. If the inductor is connected to a 2.00 ohm in parallel and then connected to a 12.0V, what is the current after 12.5ms? E. What is the maximum current that will run through the inductor if it is connected to a 12.0V battery? A. What is the characteristic time constant for the inductor? B. If it is connected to a 12.0V battery, what is the current after 12.5ms? C. If the inductor is connected to a 2.00 ohm in series and then connected to a 12.0V, what is the current after 12.5ms? D. If the inductor is connected to a 2.00 ohm in parallel and then connected to a 12.0V, what is the current after 12.5ms? E. What is the maximum current that will run through the inductor if it is connected to a 12.0V battery?

Explanation / Answer

here ,

resistance , R = 4 Ohm

inductance , L = 25 mH

A)

time constant , T = L/R

T = 0.025/4

T = 0.00625 s = 6.25 ms

the time contant is 6.25 ms

B)

as current in the circuit is

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

at t = 12.5 ms

I = (12/4) * (1 - e^-2)

I = 2.59 A

the curent is 2.59 A

C)

for resistance , Rs = 4 + 2

Rs = 6 Ohm

I = (V/R) * (1 - e^(-t*R/L))

at t = 12.5 ms

I = (12/4) * (1 - e^(-12.5 * 6/25))

I = 2.85 A

the curent is 2.85 A

D)

for resistance in parallel

1/Rp = 1/4 + 1/2

Rp = 1.333 Ohm

T = L/Rp

T = 25/1.333 = 18.75 ms

I = (12/4) * (1 - e^(-18.75/12.5))

I = 2.33 A

the current in inductor is 2.33 A

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