An ideal constant voltage source has internal resistance

Concept:

Internal resistance: 

• Internal resistance is the opposition to the flow of current inside the cells and batteries. 
• ​This internal resistance is responsible for the heating up of cells or batteries.
• The relationship between internal resistance and emf of a cell is given by:

V = E - ir

​Where E is the emf, I is current, R is the resistance of the load, V is the potential difference across the cell, and r is the internal resistance of the cell.

Explanation:

• The internal resistance is undesirable. 
• It affects the overall potential difference across the battery and the amount of current. 

In the above diagram, the external resistance is R and the current in the circuit is I.

The external resistance and the internal resistance are in series. 

By Kirchoff's Voltage Law

E = ir + iR

If there has been no internal resistance the current would have been 

Clearly, I' > I

So, current obtained is more without internal resistance. 

So, internal resistance for the ideal case is expected to be zero.