Using superposition theorem, find 'v_o' in the following circuit:

Superposition Theorem

Superposition theorem states that in any linear, bilateral network where more than one source is present, the response across any element in the circuit is the sum of the responses obtained from each source considered separately.

Keeping 18V active:

From the diagram, both the 2Ω are in parallel.

\(R={2\times 2\over 2+2}=1Ω \)

Now all the resistances are in series. So, using voltage divider rule to obtain 'v_o' :

\(v_{o1}={18}\times {1\over 1+1+4}=3V\)

Keeping 6A active:

From the diagram, both the 2Ω are in parallel.

\(R={2\times 2\over 2+2}=1Ω \)

Using current divider rule to obtain current across 1Ω:

\(i=6\times {4\over 4+1+1}=4A\)

\(v_{o2}=4\times 1=4V\)

By superposition theorem:

\(v_o={v_{o1}+v_{o2}}\)

\(v_o=3+4=7V\)