Solution:

In the given circuit of

$N$

cells, the emf (

$E_N$

) and internal resistance (

$r_N$

) are related as

$E_N = 1.5r_N$

. To find the current (

$I$

), we follow these steps:

1. Equivalent emf and resistance:
   • The cells are connected in series, so:
     $$E_{\text{eq}} = E_N = 1.5r_N, \quad r_{\text{eq}} = r_N.$$ 
2. Total resistance:
   • Let
     $R_{\text{ext}}$ 

     be the external resistance of the circuit. From the figure, the circuit resistance is: $$R_{\text{total}} = r_N + R_{\text{ext}}.$$ 

3. Ohm's Law:
   • The current in the circuit is:
     $$I = \frac{E_{\text{eq}}}{R_{\text{total}}} = \frac{1.5r_N}{r_N + R_{\text{ext}}}.$$ 
4. Condition for ( I = 1.5 , \text{A}:
   • Substituting
     $I = 1.5$ 

     into the equation: 

     $$1.5 = \frac{1.5r_N}{r_N + R_{\text{ext}}}.$$ 

   • Simplifying: 

     $$r_N + R_{\text{ext}} = r_N \implies R_{\text{ext}} = 0.$$ 

Thus, the current

$I = 1.5 \, \text{A}$

when

$R_{\text{ext}} = 0$

, meaning there is no external resistance.