What will be the value of V_{a} in the given circuit?

This question was previously asked in

DFCCIL Executive S&T 2016 Official Paper

Option 2 : 142.8 V

__Concept:__

Nodal Analysis:

Nodal analysis is a method of analyzing networks with the help of KCL equations.

For a network of N nodes, the number of simultaneous equations to be solved to get the unknowns

= Number of KCL equations

= N - 1

= one less than the number of nodes

Let a network and find voltage V using nodal analysis

Applying nodal analysis at node V

\(\frac{{V - {V_1}}}{{{R_1}}} + \frac{{V - {V_2}}}{{{R_2}}} + \frac{{V - {V_3}}}{{{R_3}}} = 0\)

By solving it we can find voltage V

__Calculation:__

Applying Nodal analysis across 10 Ω resistor:

As Va is the voltage across 10 Ω resistor

\(\frac{V_a}{10} \ + \ \frac{V_a }{25} =20\)

35V_{a} = 20 × 250

\(V_a=\frac{1000}{7}\)

**Va = 142.8 V**

Hence option (2) is the correct answer.