Question

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

Answer 1

(1) Calculation of 𝑉_𝑇𝐻
Removing the variable resistor R from the network

Mesh 1 and 2 will form A loop.
Writing current equation for the loop.
𝐼₂−𝐼₁=4 ………………..(1)
Applying KVL to the loop,
8−𝐼₁−5𝐼₁−5𝐼₂−10=0
−6𝐼₁−5𝐼₂=2 ………..(2)
From (1) and (2) we get,
𝐼₁=−2𝐴 and 𝐼₂=2𝐴
Writing 𝑉_𝑇𝐻 equation,

8−𝐼₁−𝑉_𝑇𝐻=0 => 8+2−𝑉_𝑇𝐻=0
𝐕𝐓𝐇=𝟏𝟎𝐕
(2) Calculation of 𝑅_𝑇𝐻

Replacing the voltage source by short circuits and current sources by an open circuit
𝑅_𝑇𝐻 = 10Ω || 1Ω = 0.91Ω
For maximum power transfer
(3) Calculation of 𝑃_𝑚𝑎𝑥

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