Q: Determine voltage across1k ohm resistor.

Solution:

As in the circuit 2k & 1k ohm resistors are in series and the similar current will flow through them therefore we will join them and afterwards they will become 3k ohm

therefore,

For node 1

                   (V₁ + 6)/6k + (V₁+3)/2k +V₁/3k = 0

                    6 + V₁+9 +2V₁+3V₁ = 0

                     6V₁+15 = 0

                      V₁ = - 15/6 volts

By Voltage divider rule at V₀

                    V₀ = 1/3 x -15/6

                     = -5/6 volts