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A battery of emf epsilon and internal re...

A battery of emf `epsilon` and internal resistance r is connected across a pure resistance device (e.f. and electric heater or an electric bulb) of resistance R. Show that the power output of the device is maximum when there is a perfect 'mathcing' between the external resistance adn the source resistance (i.e., where R=r). Determine the maximum power outpur.
Or
State and prove the maximum power theorem. show that the effciency of a battery when delivering maximum power is only 50%
(b) What is power output of the source abvoe if the battery is hosrted? what is the power dissipation inside the battery in that case?

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