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

given,

battery voltage = 9.9 V

resistance of the circuit = 15 Ω

Inductor = 0.9 H

a) current

`i = (V)/(R)`

`i = (9.9)/(15)`

I = 0.66 A

b) Time taken to reach current to 50%

`I = I_o (1 - e^{-(t)/(\tau)})`

`0.5 I_0 = I_o (1 - e^{-(t)/(\tau)})`

`e^{-(t)/(\tau)} = (1)/(2)`

taking log both side

t = τ ln 2

`t= (L)/(R)\ ln 2`

`t = (0.9)/(15)\ ln 2`

t = 0.0416 s