Question

in a circuit containing inductance l, resistance R and voltage E, the current i is given by : L di/dt + Ri = E Given L = 640 henry, R = 250 ohms, E = 500 volts and at t = 0, i = 0, find the time that elapses before it reaches 90% of its maximum value.

Answer 1

Answer:

As in example 1 the current is given by i=

R

E

(1−e

−Rt/L

)

As t→∞,e

−Rt/L

→0 and the current reaches its theoretical maximum value say I.

I=

R

E

when i=I/2 we get,

2

I

=I(1−e

−Rt/L

) ∴

2

1

=1−e

−Rt/L

∴e

−Rt/L

=

2

1

∴e

−Rt/L

=2

∴

L

Rt

=log2 ∴t=

R

L

log2.

Answer 2

Answer:

t=5.8946 secconds

Explanation:

See the picture attached.

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