Find the Thevenin voltage and resistance for the given circuit

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Find the Thevenin voltage and resistance for the given circuit shown below—

1. R_th = 58.82 Ω, V_th = 117.64 V
2. R_th = 117.64 Ω, V_th = 58.82 V
3. R_th = 58.82 Ω, V_th = 58.82 V
4. None of these

Correct Option: A

Calculation for R_th
As there are many dependent sources are taking into account so in order to calculate the R_th let an imaginary current source say 2A is connected across the open terminal then R_th will be the ratio of

		V_x	=	V_x
		I		2

On applying KCL at node N.

		V_x - 1000 I_x	+	V_x	+	V_x	= 2 ....(i)
		100		100		3000

Also I_X =	V_x	= I₁....(ii)
	3000

Solving equations (i) and (ii), we get
V_X = (58.82 × 2) V

so, R_th =		V_x	=	58.82 × 2	= 58.82 Ω
		2		2

(∵ R_th =	V_x	= I₁, where I = 2 amp {imaginary source})
	I

V_X = V_th = 58.82 × 2 = 117.6 V