Derive Expression for Relation Between E.M.F and Terminal Potential Difference

Notes for Derive Expression for Relation Between E.M.F and Terminal Potential Difference - Class 12 Physics Chapter 3 Electricity is prepared by our senior and renowned teachers of Param Himalaya

Consider a cell of e.m.f (E) and internal resistance (r) connected to an external resistance (R) through a key (K) as shown in figure. 

Case 1 : When key (K) is open , no current is drawn from the cell. So the voltmeter connected across the cell gives the value of e.m.f (E). 

Case 2 : When key (K) is closed , current is drawn from the cell by the circuits, which is given by 

\[I=\frac{E}{R+r}\] \[E=IR+IR\] 

Since External resistor R is connected in parallel to the electrodes of the cell, so the terminal potential difference of the cell is equal to the potential difference across the resistor R.

\[V=IR\] so \[E=V+Ir\] \[V=E-Ir\]

This shows that "The terminal potential difference of the cell is less than the e.m.f of the cell."

Now the voltmeter connected across the cell will read the value as V which is less than the value of e.m.f (E). 

If the circuit is open ,    I = 0

Hence , V= E

This , terminal potential difference between the electrodes of the cell is equal to the e.m.f of the cell in an open circuit.