A series circuit contains a 300H inductor a 520 resistor and

A series circuit contains a 3.00-H inductor, a 5.20- resistor, and a 6.50-V battery. The current is initially zero when the circuit is connected at

t = 0.

At what time will the current reach the following?

(a) 33.3% of its final value
s

(b) 95.0% of its final value
s

A series circuit contains a 3.00-H inductor, a 5.20- resistor, and a 6.50-V battery. The current is initially zero when the circuit is connected at

t = 0.

At what time will the current reach the following?

(a) 33.3% of its final value
s

(b) 95.0% of its final value
s

t = 0.

(a) 33.3% of its final value
s

(b) 95.0% of its final value
s

for Lr circuit I(t) = V/R(1-e^(-Rt/L))

a) now I(t) = 1/3 V/R

so e^(-Rt/L)= 2/3

Rt/L = -ln (2/3) = .405565

t= .405565*L/R = .405565 * 3/5.20 =.233 s

b) similarly I(t)=95/100 V/R

so e^(Rt/L) = - ln(5/100)

t =2.9957*3.5/5.20 = 1.728 s