Question

The e.m.f. of a cell is ε and its internal resistance is r. Its terminals are connected to a resistance R. The potential difference between the terminals is 1.6 V for $R=4\Omega$ and 1.8 V for $R=9\Omega$. Then,

• A. $\epsilon =1V,r=1\Omega$
• B. $\epsilon =2V,r=1\Omega$
• C. $\epsilon =2V,r=2\Omega$
• D. $\epsilon =2.5V,r=0.5\Omega$

Answer 1

The correct option is B $\epsilon =2V,r=1\Omega$

Case 1:
$V=IR$
$I=\frac{E}{r+4}$
$V=E-IR$
$1.6=E-\left(\frac{E}{r+4}\right)R$
On rearranging,
$\begin{array}{}\frac{E}{r+4}=0.4& \text{(1)}\end{array}$
Case 2:
$V=IR$
$I=\frac{E}{r+9}$
$V=E-IR$
$1.8=E-\left(\frac{E}{r+9}\right)R$
On rearranging,
$\begin{array}{}\frac{E}{r+9}=0.2& \text{(2)}\end{array}$
Equating (1) and (2), we get
$\frac{r+9}{r+4}=2$
On solving above equation,
$r=1\Omega$
Substituting this value in (1),
$\frac{E}{1+4}=0.4$
$E=2V$