A cell of emf E and internal resistance r is connected across an external resistance R. Plot a graph showing the variation of P.D. across R, verses R.

Explanation

When external resistance R is connected with cell of emf `epsilon` and internal resistance r, then p.d. between two ends of resistor ,
`V = epsilon - Ir `
`therefore V = epsilon - (V)/(R) r " " (because I = (V)/(R) )`
`therefore epsilon = V (1 + (r)/(R) ) `
`therefore V = (epsilon)/(1 + (r)/(R) ) = ( epsilon R)/(R + r) " " therefore V prop (R)/(R + r )`
`therefore V ` increases with increase in R.
Graph of V `rarr` R will be as shown.

when graph becomes parallel to R axis, then V = `epsilon and R infty`.