Find v₀ in the following circuit using the superposition theorem.

Concept:

Superposition Theorem:

• It is stated that in any linear, active, bilateral network having more than one source, the response across any element is the Algebraic sum of the response obtained from each source considered separately and all other sources are replaced by their internal resistance.
• The principle of the superposition theorem is based on Linearity.
• Voltage Source  →   short
• Current source   →  open
• Do not disturb the dependent source present in the network.

Step to solving Network by superposition theorem

• Step 1 – Take only one independent source of voltage or current and deactivate the other sources.
• Step 2 – If there is a voltage source then short circuit it and if there is a current source then just open circuit it.
• Step 3 – Thus, by activating one source and deactivating the other source find the current in each branch of the network.
• Step 4 – Now to determine the net branch current utilizing the superposition theorem, add the currents obtained from each individual source for each branch.
• Step 5 – If the current obtained by each branch is in the same direction then add them and if it is in the opposite direction, subtract them to obtain the net current in each branch.

Calculation:

Now taking 12 V voltage source

Deactivate other sources like Voltage source short circuit and current source open circuit.

Here,

5 A source → open circuited

$V_0=12\times \frac{2}{2+3+5}=2.4V$

Now taking 5A current source

Deactivate other sources like Voltage source short circuit and current source open circuit.

Here,

12 V source → Short circuited

$I=5\times \frac{5}{5+3+2}=2.5A$

V₀ = 2.5 × 2 = 5 V

From Superposition theorem

The actual V_o with both the sources will be the sum of voltages obtained in respective cases

V_o = 2.4 + 5 = 7.4 V