This question was previously asked in

LMRC Assistant Manager Electrical (SCTO) : 2018 Paper

Option 1 : Zero or 16 W

ST 1: General Awareness

7027

15 Questions
15 Marks
15 Mins

__Concept__:

Let the resistance in a circuit is R and there are two independent sources.

Let the current I_{1} is current flows through the resistor R when only one source is active and I_{2} is the current flow through the resistor R when only the other source is active.

Power consumed by R when the first source active is:

\({P_1} = I_1^2R\)

\( {I_1} = \sqrt {\frac{{{P_1}}}{R}} A\)

Power consumed by R when second source active is

\({P_2} = I_2^2R\)

\({I_2} = \sqrt {\frac{{{P_2}}}{R}} A\)

By using superposition theorem, the current flowing through the resistor R = I_{1} ± I_{2}

Now, the power consumed by resistor R will be:

\(P = {\left( {{I_1} \pm {I_2}} \right)^2}R\)

\(P = {\left( {\sqrt {\frac{{{P_1}}}{R}} + \sqrt {\frac{{{P_2}}}{R}} } \right)^2}R\)

\(= {\left( {\sqrt {{P_1}} \pm \sqrt {{P_2}} } \right)^2}\)

__Calculation__:

Given that,

P_{1} = P_{2} = 4 W

By using superposition theorem, we get:

\(P = {\left( {\sqrt {{P_1}} \pm \sqrt {{P_2}} } \right)^2}\)

\(P = {\left( {\sqrt 4 \pm \sqrt 4 } \right)^2} = 0\;or\;16\;W\)