# Word problem dealing with current and circuits

When the switch is closed in the circuit below, the current begins to build up according to the equation:

I=E/R[1-e^-(R/L)t]

where I is current in amps, t is Time in seconds

E is voltage

R is resistance in ohms and

L is inductance in henrys

V=9volts

R=10 ohms

L= 20 henrys

has an on/off switch

a) What is the maximum current in the circuit?

(hint: this value, called steady state happens at very large values of t)

b) How much current is flowing 0.50 seconds after the switch is closed?

c) At what time will the current be exactly 1/2 of the maximum value?

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#### Solution Preview

a)

The limit of e^(-x) as x goes to infinity is 0, so

lim I = (V/R) (1 - 0) = V/R = (9v)/(10o) = 0.9 ...

#### Solution Summary

This shows how to find the maximum current for a given circuit. The current which begins to build up according to the equations are given.