Explain cell, emf and internal resistance. Derive relation between potential difference emf and internal resistance.

Explanation

`rArr` As shown in figure in a glass vessel electrolyte is field in.

`rArr` In this electrolyte tw" electrode are partially dipped. One electrode is positive electrode (P) and second electrolyte is negative (N) .
`rArr` Electrodes dipped in electronde exchange electric charge in form of positive and negative ion produced as result of positive and negative ion produced as a result of chaemical reaction.
`rArr ` Potential difference between electrode A and electrolyte is `(V_(+) V_(+) gt0) ` and potential difference between electrolyte and negative electrode is `V_(-)V_(-)lt 0. `
`rArr` When current is not flowing in the circuit potential drift between two point P and N.
` V_(+) - (V_(-))`
= `V_(+) + V_(-)`
`rArr` Potential difference between `V_(+) and V_(-) ` is called electromotive force (emf) of the cell, it is denoted by `epsilon`.
`epsilon = V_(+) + V_(-) gt 0 ` .... (1)
`rArr ` Definition of emf of cell : " When unit positive charge moves from negative to positive terminal of cell due to non electric force then energy gained by charge is called emf of cell. "
`. epsilon. ` is not force force but it is potential difference.
`rArr` Consider resistor R connected to cell as shown in figure.
`rArr ` In resistor R, current I flows from C to D.
`rArr ` In electrolyte steady current flows from negative terminal (N) to positive tenninal (P) and in resistance current Hows from P to N.
`rArr` If resistance R is infinite then,
`I = (V)/(R) = (V)/("infinite" ) = 0 `
where, V is potential difference between P and N.
`therefore V = `[p.d. between p and N [ +
[ p.d. between A and B ] +
[ p.d. between B and N]
= `V_(+) + (-Ir) + V_(-)`
`= V_(+) + V_(-) - Ir`
`epsilon = V_(+) + V_(-)`
In open circuit condition,
I = 0
`therefore V = epsilon`
`rArr " " ` Thus, `epsilon` is potential difference between positive and negative electrode.
`rArr` If R be finite resistance of the circuit then potential difference between P and N ,
V = `epsilon - 1r" " ` ...(2)
`rArr` Practically If `epsilon gt ` Ir then internal resistance of cell can be neglected.
`rArr ` For different cell internal resistance is of different value .
`rArr` Internal resistance of dry cell is large compared to internal resistance of electrolytic cell.
`rArr` When current I flows through R, then p.d. between two end of resistance,
V = IR `" "` ... (3)
from equation (2) and (3)
IR = `epsilon`- Ir
or I = `(epsilon)/(r + R)`
when R = 0 maximum current tlow through cell.
`therefore I_("max") = (epsilon)/(R)`
Remember :
(1) When cell is not in use then,
V = `epsilon `
(2) In case of open circuit condition,
` V = epsilon `
(3) When cell is in use , ` ( V lt epsilon)`
(4) When cell is being charged, `(V gt epsilon)`
`therefore V = epsilon + Ir `