This question was previously asked in

DSSSB JE EE 2015 Official Paper (Held on 31 May 2015)

Option 4 : both (2) and (3)

According to Kirchhoff’s voltage law (KVL), the algebraic sum of all the voltages around any closed path is zero. It is based on the conservation of energy.

\({V_1} + {V_2} + {V_3} + \; \ldots \ldots \ldots .\; + {V_n} = 0\) or \(\mathop \sum \limits_{n = 1,2,3 \ldots .} V = 0\)

**It is also known as the loop current method of analysis. It is concerned with both IR drop and battery emf.**

__Additional Information__

There are two types of Kirchoff’s Laws:

Kirchoff’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.

Kirchoff’s second law:

- This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic 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).

Here, the assumed current I causes a + ve drop of voltage when flowing from +ve to – ve potential while – ve drop of voltage when a current flowing from – ve to + ve for the above circuit,

If we apply KVL,

−V + I R1 + I R2 = 0

So, the **algebraic sum of all IR drops and battery e.m.f.s in any closed loop of a network is always zero.**