Consider the circuit shown in the figure.



The value of v₀ (rounded off to one decimal place) is ______ V.

In the range: 1 - 1

Concept:

There are two types of Kirchhoff’s Laws :

Kirchhoff’s first law :

- This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.



- In a circuit, at any junction, the sum of the currents entering the junction must be equal the sum of the currents leaving the junction i.e., i1 + i3 = i2 + i4
- This law is simply a statement of “conservation of charge” as if current reaching a junction is not equal to the current leaving the junction, charge will not be conserved.

Kirchhoff’s second law:

- This law is also known as loop rule or voltage law (KVL) and according to it “thealgebraic sum of the changes in potential in the complete traversal of a mesh (closed-loop) is zero”, i.e. Σ V = 0.
- This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.
- If there are n meshes in a circuit, the number of independent equations in accordance with loop rule will be (n - 1).

Analysis:

Given circuit diagram is redrawn as:



Consider current I in the branch BC.

Applying KCL at node B:

V${}_A$ = V${}_B$ = V₀

$\frac{V_0-4}{1}+\frac{V_0}{1}+I=6$

2V0 + I = 10 ---(1)

Applying KCL at node C:

I = 6 + 2

I = 8 mA

Putting value of I in (1), we get:

2V₀ + 8 = 10

V₀ = 1 V