Question

An inductor with an inductance of 2.30 H and a resistance of 7.50 ? is connected to the terminals of a battery with an emf of 6.00 V and negligible internal resistance.

(a) Find the initial rate of increase of current in the circuit.
A/s

(b) Find the rate of increase of current at the instant when the current is 0.500 A.
A/s

(c) Find the current 0.250 s after the circuit is closed.
A

(d) Find the final steady-state current.
A

Answer 1

given

L=2.3 H

R=7.5 ohm

emf E=6 v

a)

by using kirchhoff law

E-L(di/dt)-iR=0

di/dt=(E-iR)/L

initially i=0

di/dt=E/L

=6/2.3

=2.608 A/sec

b)

di/dt=(E-iR)/L

di/dt=(6-0.5*7.5)/2.3

=0.978 A/sec

c)

i=io[1-e^-(R/L)*t]

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

=6/2.3[1-e^-(7.5/2.3)*0.25]

=1.45 A

d)
imax=E/R

=6/2.3

=2.608 A