Answer:
The EMF of each battery is 6 volts and the EMF of two batteries connected in series is 12 volts.
Explanation:
According to the Kirchhoff's Voltage Law, net voltage of a closed circuit must be zero. That is:
[tex]\Sigma \limits_{i=1}^{n} V_{i} = 0[/tex] (1)
Where [tex]V_{i}[/tex] is the voltage of the i-th component of the closed circuit, measured in volts. Please notice that voltage for a power generating element (i.e. EMF) is less than zero and for a power consuming element is greater than zero (i.e. Batteries being charged by the EMF). In addition, if n-elements are connected in series, then the equivalent voltage is:
[tex]V_{eq} = \Sigma\limits_{i = 1}^{n} V_{i}[/tex] (2)
Let consider that closed system is formed by two batteries connected in series and an EMF, by (1) and (2) we have that:
[tex]V_{EMF} - V_{eq,batt} = 0[/tex]
[tex]V_{EMF} = V_{1}+V_{2}[/tex] (3)
If we know that [tex]V_{1} = V_{2} = 6\,V[/tex], then the EMF of the battery is:
[tex]V_{EMF} = 12\,V[/tex]
The EMF of each battery is 6 volts and the EMF of two batteries connected in series is 12 volts.
