What maximum power can be obtained from a battery of emf `epsilon` and internal resistance r connected with an external resistance R ?

Options

A. `(epsilon^(2))/(4r)`
B. `(epsilon^(2))/(3r)`
C. `(epsilon^(2))/(2r)`
D. `(epsilon^(2))/(r)`

Answer

A

Explanation

`(epsilon^(2))/(4r)`
Current in circuit I = `(epsilon)/(R + r) `

If we get maximwn power through battery then external resistance becomes R = r.
`therefore " power P " = I^(2) R = (epsilon R)/((R + r)^(2)) `
`= (epsilon^(2) r)/((2r)^(2)) [ because " Putting R " = r]` ,
` = (epsilon^(2))/(4r)`