Complete Question 
A power supply has an open-circuit voltage of 40.0 V and an internal resistance of 2.00  . It is used to charge two storage batteries connected in series, each having an emf of 6.00 V and internal resistance of 0.300
. It is used to charge two storage batteries connected in series, each having an emf of 6.00 V and internal resistance of 0.300 . If the charging current is to be 4.00 A, (a) what additional resistance should be added in series? At what rate does the internal energy increase in (b) the supply, (c) in the batteries, and (d) in the added series resistance? (e) At what rate does the chemical energy increase in the batteries?
 . If the charging current is to be 4.00 A, (a) what additional resistance should be added in series? At what rate does the internal energy increase in (b) the supply, (c) in the batteries, and (d) in the added series resistance? (e) At what rate does the chemical energy increase in the batteries?
Answer:
a
The additional resistance is 
b
The rate at which internal energy increase at the supply is 
c
The rate at which internal energy increase in the battery  is  
d
The rate at which internal energy increase in the added series resistance is  
e
the increase rate of the chemically energy in the battery is 
Explanation:
From the question we are told that 
     The  open circuit voltage is  
      The internal resistance is 
      The emf of each battery is 
       The internal resistance of the battery is  
       The  charging current is  
Let assume the the additional resistance to to added to the circuit is  
  So this implies that 
         The total resistance in the circuit is 
                               
Substituting values 
                              
And  the difference in potential in the circuit is  
                          
                  =>   
                         
Now according to ohm's law 
             
Substituting values 
             
         
Making  the subject of the formula
 the subject of the formula 
 So    
            
The  increase rate of   internal energy at the supply is mathematically represented as 
         
Substituting values
      
      
The  increase rate of   internal energy at the batteries  is mathematically represented as 
          
 Substituting values
          
          
The  increase rate of  internal energy at the added  series resistance  is mathematically represented as 
         
 Substituting values
        
       
Generally the increase rate of the chemically energy in the battery is  mathematically represented as 
          
Substituting values 
        
       