Question
A variable resistor R, electromotive force and internal resistance $r$ are joined as shown in the given figure across the ends of the cell. Draw graph to show (i) terminal voltage and (ii) current $I$ as a function of $R$.
✓
Answer
Current in circuit
$ I=\frac{E}{R+r}=\frac{E}{R\left(1+\frac{r}{R}\right)} $
and terminal voltage
$V = IR$
$V =\frac{ E \times R }{ R \left(1+\frac{r}{ R }\right)}=\frac{ E }{\left(1+\frac{r}{ R }\right)}$
$ I=\frac{E}{R+r}=\frac{E}{R\left(1+\frac{r}{R}\right)} $
and terminal voltage
$V = IR$
$V =\frac{ E \times R }{ R \left(1+\frac{r}{ R }\right)}=\frac{ E }{\left(1+\frac{r}{ R }\right)}$
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