= Solution
Let $C_T=C+C_1$ be the total parallel <capacitance>, since <capacitors> in a <parallel circuit> have additive <capacitances>. Put $\omega_*=2\pi(50\,\mathrm{Hz})$ into the <lossy parallel coil resonance> condition:
$$
C_T=\frac{L}{R^2+\omega_*^2L^2}=\frac{0.150}{10^2+[2\pi(50)(0.150)]^2}\,\mathrm F=64.6368\,\mu\mathrm F.
$$
The additional <capacitance> is therefore
$$
\boxed{C_1=C_T-C=64.6368-10.0000=54.6368\,\mu\mathrm F\simeq54.6\,\mu\mathrm F.}
$$
This is the added <capacitance>, rather than the new total, and the conversion from <frequency> to <angular frequency> is essential.
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