Correct Option: C

I =	V1∠δ - V2∠0
	Z∠θ

=	V1	∠(δ - ∠0) -	V2	∠- θ
	Z		Z

Power received, P₂ = Re [V₂I*]

= Re		V2		V1	∠(θ - δ) -	V2	∠θ
				Z		Z

=	V1V2	cos(θ - δ) -	V²2	cos θ
	Z		Z

Let θ = 90° – α, then

=	V1V2	cos(90° - α - δ) -	V²2	cos(90° - α)
	Z		Z

=	V1V2	sin(α + δ) -	V²2	sin α
	Z		Z

P2 max =	V1V2	-	V²2	sin α[α + δ = 90°]
	Z		Z

As, sin α =	r	, then
	Z

P2 max =	V1V2	-	V²2	.	r
	√r² + x²		√r² + x²		√r² + x²

For P_{2 max} to be maximum,

dP2 max	= 0
dx

or V²2		x1	-	2xr		= 0
		(r² + x²)2/3		(r² + x²)²

Here V₁ = V₂
∴ r² + x² = 4r²
or x = √3r