Test: Basic Nodal & Mesh Analysis- 2 - Electrical Engineering (EE) MCQ

The given circuit can be reduced by combining resistors and current sources as shown below.

Let the node voltage be V volts.
Applying nodal analysis, we have

or, 
or, 
or, 5 + 
or, 
or, 
So, 

If the equivalent resistance of first figure is RA then from the second figure, we can see that
R_B=R_A||1Ω.
R_B= R_A /(1+R_A)

Applying nodal analysis at the given node, we have

or, 3I_x = V - 3 ...(i)
Also, 10 = 2I_x + V
or, V = 10 - 2I_x ...(ii)
Putting V from equation (ii) into equation (i),
3I_x = 10 - 2I_x - 3
or, 5I_x = 7
or, 

Let the node voltage be V' volts.
Applying nodal analysis at the given node, we have

or, 2V' = 0
or, V' = 0 volts
Now, V' = - 3 + 1₁
or, 0 = - 3 + V₁
or, V₁ = 3 volts

The given circuit can be redrawn as shown below (By combining current sources).

Now, I = 0 (Given)
i.e. 
or, R = 2Ω

Node potential is always higher than the other voltages appearing in the equations otherwise a negative value for current would result.

We have,