You have a spool of copper wire that has resistance per unit

You have a spool of copper wire that has resistance per unit length 5.5 × 103 Ohms per meter and inductance per unit length of 0.30 µH per meter. Suppose you take 20.0 cm of this wire and connect the ends to the terminals of a 1.5 Volt battery. How long does it take for the current in the wire to reach 80.% of its maximum value?

Please show work.

Solution

Resistance

R=(5.5*10^-3)(0.2) =1.1*10^-3 ohms

Inductance

L=0.3*0.2 =0.06 uH

Time Constant

T=L/R =(0.06*10^-6)/(1.1*10^-3) =54.54us

RL Circuit current charging equation is given by

I=I_max[1-e^-t/T]

Given I/I_max=0.8

=>0.8 =[1-e^-t/54.54us]

Ln(0.2) =-t/54.54 us

t=87.8 us =88 us(approx)