For the circuit shown below, the Vout =?

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For the circuit shown below, the V_out =?

1. 6V
2. – 6V
3. 4V
4. – 4V

Correct Option: A

The given circuit:

Applying nodal equation for supernode

V_in	+	V_out	+	V_out - 2	= 2
2		2		2

or
V_in + 2 V_out = 6 . . . . …(i)
Again writting constraint equation for the dependent source inside the supernode. The dependent source voltage inside the supernode must satisfy.
V_in – V_out = 4i₁
or
V_in – V_out = 4 V_in/2
or
V_in + V_out = 0 . . . …(ii)
From equation (i) and (ii) we get
V_out = 6V.