Question

It takes 2.95 ms for the current in an LR circuit to increase from zero to 0.85 its maximum value.

Part A

Determine the time constant of the circuit.

Express your answer to two significant figures and include the appropriate units.

τ =

Part B

Determine the resistance of the circuit if L = 22.0 mH .

Express your answer to two significant figures and include the appropriate units.

R =

Answer 1

In LR circuit :

time taken, t = 2.95 ms = 2.95 x 10^-3 sec

change in current, I / I₀ = 0.85 A

Part-A : The time constant of the circuit is given as -

using an equations,   I = I₀ (1 - e^{-t /} )    { eq. 1 }

I / I₀ = (1 - e^{-t /} )

inserting the values in above eq.

(0.85 A) = 1 - e^{(-2.95 x 10^-3 / )}

e^{(-2.95 x 10^-3 / )} = 1 - (0.85 A)

e^{(-2.95 x 10^-3 / )} = 0.15 A

(-2.95 x 10^-3 sec) / = log (0.15)

(-2.95 x 10^-3 sec) / = -1.897

= (2.95 x 10^-3 sec) / (1.897)

= 1.5 x 10^-3 sec

= 1.5 ms

Part-B : the resistance of the circuit is given as -

time constant, = L / R                              { eq.2 }

where, L = inductance = 22 mH = 22 x 10^-3 H

inserting the values in eq.2,

(1.5 x 10^-3 s) = (22 x 10^-3 H) / R

R = (22 x 10^-3 H) / (1.5 x 10^-3 s)

R = 14.6