Question

If I is the current in the external resistor R and r is the internal resistance of the cell, the equation for the whole circuit is:

            E = I(R + r)          …….(i)

            For the same current in the external resistor R, the terminal voltage is given by:

            V = IR                  …….(ii)                                                                

        Use equations (i) and (ii) to solve for r by eliminating I and write this equation the form:   y = mx + b

Identify the independent variable and the dependent variable

Where V is the dependent variable and R is the independent variable

Answer 1

Given that

$E=I\left ( R+r \right )\: \: \: \: \: \: \: \: \: \: \: (i)$

Here R is the external resistance, r is the internal resistance and V is the terminal voltage across R.

Now by elimination I from the equation we can get

$E=I\left ( R+r \right )$

$or\: \: \: \: \: \: \: E=\frac{V}{R}\left ( R+r \right )$

$or\: \: \: \: \: \: \: E=V+\frac{r}{R}$

  $or\: \: \: \: \: \: \: \frac{r}{R}=E-V$

  $\therefore \: \: \: \: \: \: \: r=\left ( E-V \right )R$

Here r is the dependent variable and depends on R, R is the independent variable.

=l r=/E-V)R R \ K

Here b=0 (constant). y=r (dependent) ,m=(E-V)(slope), x=R(independent).