Question

The magnetic field at a point inside a 2.0 mH inductor- coil becomes 0.80 of its maximum value in $20\mu s$ whent the inductor is joined to a battery . Find the resistance of the circuit.

Answer 1

$l=l=i_0(1-e^{-\frac{t}{\tau }}){\mu }_{0}ni={\mu }_{0}n{i}_0(1-e^{-\frac{t}{\tau }})\Rightarrow B=B_0(t-e^{-t\frac{R}{L}})\Rightarrow 0.8B_0=B_0(1-e^{\frac{-20\times {10}^{-6}R}{2\times {10}^{-3}}})\Rightarrow B=B_0=(1-e^{-\frac{R}{100}})\Rightarrow e^{-\frac{R}{100}}=0.2\Rightarrow In\left(e^{-\frac{R}{100}}\right)=In\left(0.2\right)-\frac{R}{100}=-1.609\Rightarrow R=160.9=160\Omega$