What will be the value of Rth between A and B for the given

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What will be the value of R^th between A and B for the given circuit shown below?

1. 2 R
2. R (1 – J)
  2
3. R (J – 1)
  2
4. R

Correct Option: D

R_th can be calculated by opening the load terminal and all the energy sources replaced by their internal resistance the circuit becomes

R_th = R || JR + R || – JR

=		R. JR	+	R (–JR)	=	JR	-	JR
		R + JR		R - JR		(1 + J)		(1 - J)

=		JR [1 – J – (1 + J)]	=	JR [– J – 1 – J]
		1 + J²		1 – (–1)

=		JR (–2J)	=	– 2R J2	= R
		2		2