In the circuit shown, ${\mathrm{X}}_{\mathrm{C}}=100 \mathrm{\Omega }, {\mathrm{X}}_{\mathrm{L}}=200 \mathrm{\Omega } \text{and} \mathrm{R}=100 \mathrm{\Omega }$. The maximum  current through the source is $\mathrm{P}\sqrt{2} \mathrm{A}$. What is the value of ‘P’?

Phasor diagrams:

In L-C branch, the phase angle between total voltage and current is $90°$.

In the branch with only resistor, voltage and current are in phase. 

As the L-C branch and the R branch are in parallel, the voltage across both branches is same and the currents through both branches have $90°$ phase angle between them.

Therefore, current through source $\mathrm{I}=\sqrt{{\mathrm{I}}_1^2+{\mathrm{I}}_2^2}$.

Here, maximum current through L-C branch, ${\mathrm{I}}_1=\frac{\mathrm{V}}{{\mathrm{X}}_{\mathrm{L}}-{\mathrm{X}}_{\mathrm{C}}}=\frac{200}{200-100}=2 \mathrm{A}$,

and the maximum current through R branch, ${\mathrm{I}}_2=\frac{\mathrm{V}}{\mathrm{R}}=\frac{200}{100}=2 \mathrm{A}$.

Total maximum  current through source, $\mathrm{I}=\sqrt{2^2+2^2}=2\sqrt{2} \mathrm{A}$.

$\therefore \mathrm{P}=2$.