What is the power loss in the 10 Ω resistor in the Network shown in figure?

This question was previously asked in

ISRO Scientist EC 2017 (May) Official Paper

Option 2 : 15.13 W

ISRO Scientist ECE: 2020 Official Paper

361

80 Questions
240 Marks
90 Mins

The given circuit diagram can be redrawn as shown below

By nodal analysis,

KCL at V1:

\(\begin{array}{l} \frac{{{V_1}}}{3} + \frac{{{V_1} - 15}}{8} + \frac{{{V_1} - {V_2}}}{5} = 0\\ \Rightarrow 79{V_1} - 24{V_2} = 225 \end{array}\)

KCL at V2:

\(\begin{array}{l} \frac{{{V_2} - {V_1}}}{5} + \frac{{{V_2}}}{2} + \frac{{{V_2} - 15}}{{10}} = 0\\ \Rightarrow 8{V_2} - 2{V_1} = 15 \end{array}\)

By solving above two equations, V1 = 3.69 V, V2 = 2.79 V

Voltage across 10 Ω resistor = 15 – V2 = 15 – 2.79 = 12.21 V

Power loss in the 10 Ω resistor,

\(P = \frac{{{V^2}}}{R} = \frac{{{{12.21}^2}}}{{10}} = 14.9\;W\)

The most appropriate choice is 15.13 W