Illustration :    Determine the voltage across a 12K ohm resistance. When we don't  know the  current in the circuit.  

Solution

In this circuit we have three nodes one is reference node while the other node  is between the 6v battery and the 12K resistance here we will neglect this node and calculate the voltage at point A  so the node equation for the node V₁ is

At node (1)

         (V₁ - 12)/6k + (V₁ -6)/12k +V₁/6k = 0

                                                        5V₁ = 30

                                                          V₁ = 6volts

As we know that we want to calculate the voltage across 12K resistor and it is between 6V battery and V1

So,    

                                                            V₀ = V₁ - V_s

In the above equation V_s =6V

                      V₀ = V₁ -6

                           = 0 volts