Power Factor Correction

In an assignment I was asked to improve the power factor of a certain circuit to 1. The supply is 240V peak-to-peak @ 60Hz. Rs = 58 ohm, Rl = 2 ohm and L = 8 mH. Below are my calculations but I can't seem to get the right answer. Indicating where I am going wrong would be a huge help :)

• \$X_L = 2 \pi f L = 3.0159j\Omega\$


• \$Z = 60 + 3.0159j = 60.0758 \angle 2.8776 \$


• 
  

  \$I = \Large{\frac{240}{60.0758}} = \normalsize 3.995 A\$

  
  



• 
  

  True Power = \$I^2 * R = 15.9596 * 60 = 957.576 W\$

  
  


• Reactive Power = \$I^2 * X = 15.9596 * 3.0159 = 48.1326 VAR\$


• Apparent Power = \$I^2 * Z = 15.9596 * 60.0758 = 958.7857 VA\$

Then for the capacitor:

• \$X_C = \Large\frac{V^2}{Q} = \frac{57600 }{ 48.1326 }= \normalsize1196.6941 \Omega\$


• \$C = \Large\frac{1}{ 2 \pi f X_C} = \frac{1 }{ 2 \pi * 60 * 1196.6941} = \normalsize2.3557 nF\$

But this value for the capacitor seems way too small :/ Thanks for any help!