The power generated by the battery is Ei where E is the e.m.f and i is the current flowing through the battery.The power dissipated in the external resistors are i2R where R is the total external resistance 1,2 and 3.
The power dissipated in the the battery is i2r where r is the internal resistance of the battery. The power generated is equal to the total power dissipated in the battery and the external resistors. The power loss in the battery is normally regarded as wasted energy and therefore efficiency of the battery is just the ratio of the power dissipated in the external resistor to the power generated by the battery.
