Assuming both the voltage sources are in phase, the value

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

Power transferred from circuit A to circuit B

P = VI =		7		.		6 + 10R		=	42 + 70R
		R + 2				R + 2			(R + 2)²

I =	10 - 3	=	7
	2 + R		2 + R

V = 3 + IR = 3 +	7R	=	6 + 10R
	2 + R		2 + R

∴	dP	=	(R + 2)²(70) - (42 + 70R) 2 (R + 2)	= 0
	dR		(R + 2)⁴

⇒ 70(R + 2)² = (42 + 70R) 2 (R + 2)
⇒ 5(R + 2) = 2(3 + 5R)
⇒ 5R + 10 = 6 + 10R
4 = 5R
⇒ R = 0.8 Ω