Determine the value of R for maximum power transfer and find the value of maximum transfer.

#### Solution

(1) Calculation of π_{ππ»}

Removing the variable resistor R from the network

Mesh 1 and 2 will form A loop.

Writing current equation for the loop.

πΌ_{2}−πΌ_{1}=4 ………………..(1)

Applying KVL to the loop,

8−πΌ_{1}−5πΌ_{1}−5πΌ_{2}−10=0

−6πΌ_{1}−5πΌ_{2}=2 ………..(2)

From (1) and (2) we get,

πΌ_{1}=−2π΄ and πΌ_{2}=2π΄

Writing π_{ππ»} equation,

8−πΌ_{1}−π_{ππ»}=0 => 8+2−π_{ππ»}=0

πππ=πππ

(2) Calculation of π
_{ππ»}

Replacing the voltage source by short circuits and current sources by an open circuit

π
_{ππ»} = 10Ω || 1Ω = 0.91Ω

For maximum power transfer

(3) Calculation of π_{πππ₯}

`P_(max)=(V_(TH)^2)/(4R_(TH))=10^2/(4xx0.91)=27.47w`