Question

Att= 0, a 9.9 V battery is connected to aseries circuit containing a 15 Ω resistor and a0.9 H inductor.What will be the current in the circuit, along time after the circuit is established?Answer in units of A.040 (part 2 of 2) 10.0 pointsHow long will it take the current to reach50 percent of its final value?Answer in units of s.

Answer 1

Answer

given,

battery voltage = 9.9 V

resistance of the circuit = 15 Ω

Inductor  = 0.9 H

a) current

$i = \dfrac{V}{R}$

$i = \dfrac{9.9}{15}$

I = 0.66 A

b) Time taken to reach current to 50%

 $I = I_o (1 - e^{-\dfrac{t}{\tau}})$

 $0.5 I_0 = I_o (1 - e^{-\dfrac{t}{\tau}})$

 $e^{-\dfrac{t}{\tau}} = \dfrac{1}{2}$

taking log both side

t = τ ln 2

$t= \dfrac{L}{R}\ ln 2$

$t = \dfrac{0.9}{15}\ ln 2$

t  = 0.0416 s