Answer :
The value of [tex]\( R_{L} \)[/tex] for maximum power transfer is 7.7 kilo ohms.
To determine the value of [tex]\( R_{L} \)[/tex] in kilo ohms for maximum power transfer, we can use the concept of maximum power transfer theorem.
According to this theorem, the maximum power is transferred from a source to a load when the resistance of the load matches the resistance of the source.
In this case, the given resistor [tex]\( R \)[/tex] has a value of 7.7 kilo ohms.
To find the value of [tex]\( R_{L} \)[/tex] for maximum power transfer, we need to match the resistance of [tex]\( R_{L} \)[/tex] with [tex]\( R \)[/tex].
To do this, we can set up the equation:
[tex]\( R = R_{L} \)[/tex]
Since [tex]\( R \)[/tex] is given as 7.7 kilo ohms, we can substitute this value into the equation:
[tex]\( 7.7 \, \text{kilo ohms} = R_{L} \)[/tex]
Therefore, the value of [tex]\( R_{L} \)[/tex] for maximum power transfer is 7.7 kilo ohms.
It's important to note that the value of [tex]\( R_{L} \)[/tex] for maximum power transfer is not dependent on any other information provided in the question.
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