Given:

$C = 20μf \\ I = 0.345A \\ V_{coil} = 40V \\ V_c=55V \\ V_{R-Coil}=50V \\ \text{Supply voltage} \\ R= \dfrac{V_R}{I}=\dfrac{25}{0.345}=72.46Ω \\ Z_{coil}=\dfrac{V_coil}{I}=\dfrac{40}{0.345} =115.94Ω \\ X_C=\dfrac{V_C}{I}=\dfrac{55}{0.345}=159.42 \\ Z_{R-Coil}=\dfrac{V_{R-Coil}}{I}=\dfrac{50}{0.345}=144.92 \\ Z_{Coil}=\sqrt{r^2+X_L^2}=115.94 \\ r^2+X_L^2=13442.08 \\ Z_{R-Coil}=(R+r)+jX_L \\ Z_{R-Coil}=\sqrt{(R+r)^2+X_L^2 )} \\ 144.92^2=(72.46+r)^2+X_L^2 \\ 13206.6=(72.46+r)^2+X_L^2 \\ \text{Subtracting (2) from (1) we get,} \\ r^2+X_L^2-(72.46+r)^2-X_L^2=13442.08-1320.66 \\ r^2-(5250.45+144.92r+r^2 )=235.48$