SSE JE Electrical Engineering 28 Oct 2020 Shift 1 Papers

Self-inductance of coil 1 $\left({\mathit{L}}_1\right)$ = 15 mH
Let the self-inductance of coil 2 is ${\mathit{L}}_2$
Let the mutual inductance is M
Total inductance in case of series addition = 70 mH
$\Rightarrow 15+{\mathit{L}}_2+2\mathit{M}=70$
$\Rightarrow {\mathit{L}}_2+2\mathit{M}=55$
Total inductance in case of series opposition = 30 mH
$\Rightarrow 15+{\mathit{L}}_2-2\mathit{M}=30$
$\Rightarrow {\mathit{L}}_2-2\mathit{M}=15$
From the above two equations,
${\mathit{L}}_2=35\mathrm{mH}$