Question

If 2.2kW power is transmitted through \[10{\rm{ }}\Omega \] line at \[22{\rm{ kV}}\], power loss in the form of heat will be
A. \[0.1{\rm{ W}}\]
B. \[1{\rm{ W}}\]
C. \[0.01{\rm{ W}}\]
D. \[10{\rm{ W}}\]

Answer 1

Hint: The concept of power transmitted through the line gives the relationship between power transmitted, voltage, current, and power factor of that line. Also, the concept of power loss gives the relation between power loss, current, and resistance. We will be using both concepts to determine how much power is lost in the form of heat.

Complete step by step answer:
Given:
Power transmitted power through the line is \[P = 2.2{\rm{ kW}}\].
The resistance of the line is \[R = 10{\rm{ }}\Omega \].
The voltage of the line is \[V = 22{\rm{ kV}}\].
We have to find the power loss in the form of heat.
Let us write the expression for power transmitted through the given wire.
\[P = VI\cos \phi \]……(1)
Here \[\cos \phi \] is the power factor of the given line.
We know that the value of the power factor for a fully resistive circuit is unity.
\[\cos \phi = 1\]
Substitute \[1\] for \[\cos \phi \] in equation (1).
\[\begin{array}{c}
P = VI\left( 1 \right)\\
 = VI
\end{array}\]
Rearrange the above expression such that the expression for current I will be obtained.
\[I = \dfrac{P}{V}\]
Substitute \[2.2{\rm{ kW}}\] for P and \[22{\rm{ kV}}\] for V in the above expression.
\[\begin{array}{c}
I = \dfrac{{2.2{\rm{ kW}}}}{{22{\rm{ kV}}}}\\
 = 0.1{\rm{ A}}
\end{array}\]
We know that the power loss in the line is equal to the product of the square of current and voltage.
\[{P_L} = {I^2}R\]
Here \[{P_L}\] is the loss of power in the wire.
Substitute \[0.1{\rm{ A}}\] for I and \[10{\rm{ }}\Omega \] for R in the above expression.
\[\begin{array}{c}
{P_L} = {\left( {0.1{\rm{ A}}} \right)^2}\left( {10{\rm{ }}\Omega } \right)\\
 = 0.1{\rm{ W}}
\end{array}\]
Therefore, the loss of power in the form of heat is \[0.1{\rm{ W}}\] when \[2.2{\rm{ kW}}\] power is transmitted through \[10{\rm{ }}\Omega \] line at \[22{\rm{ kV}}\]

So, the correct answer is “Option A”.

Note:
We do not have to evaluate the unit of power unnecessarily because we know the power unit is Watt, but extra attention is required when units are in its subsequent multiples such as kilo, as given in the question. Heat and electrical power are two forms of energy where heat is thermal energy and electrical power is electrical energy.