Question

A cell of e.m.f. $\epsilon$ and internal resistance r sends current 1.0 A when it is connected to an external resistance 1.9 $\Omega$ but it sends current 0.5 A when it is connected to an external resistance $3.9\Omega$. Calculate the values of $\epsilon$ and r.

Answer 1

Case I:

$I=1AR=1.9\Omega$

So, $\epsilon =I(R+r)=1(1.9+r)\Rightarrow \epsilon =1.9+r...\left(i\right)$

Case II:

$I^{\prime }=0.5A{R}^{\prime }=3.9\Omega$

So, $\epsilon =I^{\prime }(R^{\prime }+r)=0.5\times (3.9+r)\Rightarrow \epsilon =1.95+0.5r...\left(ii\right)$

From (i) and (ii), $1.9+r=1.95+0.5r\Rightarrow 0.5r=0.05\Rightarrow r=0.1\Omega$

and $\epsilon =1.9+r=1.9+0.1=2V$