59 and 61

59 and 61 to ROA

Dear Student,
                     61,
                     $$\begin{gathered} Resis\tan ce of the coil=\frac{{V^2}_{dc}}{W}=\frac{{10}^2}{20}=5ohm \\ power loss when current is ac \\ 10=\frac{{V^2}_{ac}}{Z}\cos \left(\phi \right)=\frac{{10}^2}{\sqrt{{\left(5\right)}^2+(\omega \times .01{)}^2}}\times \frac{5}{\sqrt{{\left(5\right)}^2+(\omega \times .01{)}^2}} \\ \omega =500 \\ f=\frac{500}{2\times 3.14}=80Hz \end{gathered}$$
Kindly post different question in different threads 
Regards