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Derive the condition for maximum power transfer through the network.

written 3.5 years ago by teamques10 ★ 68k

modified 3.0 years ago by pedsangini276 • 4.8k

basic electrical engineering

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written 3.5 years ago by teamques10 ★ 68k

$P_2= \dfrac{V^2 _{th}.R_2}{(R_{th}+R_2)^2}$ $\Rightarrow$ At $P_{max}$, $\frac{dP}{dR_2} = 0$

$\therefore V_{th}^2[(R_{th}+R_L)^2-2R_L(R_{th}+R_2)]=0\\ \therefore R_{th}^2 +R_{L}^2+2R_{th}.R_L-2R_{L}.R_{th}-2R_{L}^2=0$

$\therefore R_{th}^2 = R_{L}^2\Rightarrow R_{th} =R_{L}$ ..... Condition for $P_{max}$

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