Question

state and prove maximum power transfer theorem

Answer 1

For instance, the outer electrons of the atoms in wool are held more loosely than the outer electrons of the atoms in a plastic ruler. ... If a rod made of Perspex is rubbed on a cotton cloth, an electric charge is also produced on the rod.

Answer 2

$\huge{\underline{\underline{\bold{\mathtt{\purple{♬A{\pink{N{\green{S{\blue{W{\red{E{\orange{R♬}}}}}}}}}}}}}}}}$

Maximum Power Transfer Theorem:

"Load resistor recieves maximum power from source only when the resistance of load is equal to internal resistance of the source"

Consider a load resistance RL connected across a source of voltage V and internal reisitance Rs

Let エ be the current flowing through circuit RL

PL ➝ Power recieved by load

Then

${\huge{\boxed{\tt{\color{blue}{ᴘ _{ʟ} = {ɪ}^{2} \times ʀ _{ʟ}➝(1)}}}}}$

Here total resistance of circuit Rt

$ʀ _{ᴛ} = Ʀ _{ន} + Ʀ _{ន}$

Total current in circuit is

$ɪ = \frac{ᴠ}{ʀᴛ} \\ \\ = \frac{ᴠ}{Ʀ _{ន} + Ʀ _{ʟ } } \\ \\ {\huge{\boxed{\tt{\color{blue}{ᴘ _{ʟ} = \frac{ᴠ}{Ʀ _{ន} + Ʀ _{ʟ} } \times ʀ _{ʟ}}}}}}$

According to MPT

PL becomes PL maximum

$ᴘ _{ʟ} = ( \frac{ᴠ}{Ʀ _{ន} + Ʀ _{ន} } {)}^{2} \times Ʀ _{ន} \\ \\ = ( \frac{ᴠ}{2Ʀ _{ {ន}^{2} } } ) \timesƦ _{ន} \\ = \frac{ {ᴠ}^{2} }{4Ʀ _{ន} } \\ \\[tex]{\huge{\boxed{\tt{\color{blue}{ᴘ _{ʟ }( ᴍᴀХɪᴍᴜᴍ ) = \frac{ᴠt {h}^{2} }{4 \: Ʀth}}}}}}[\tex]$

_____________________________________

Eat 5 star do nothing