When a light bulb is connected across the terminals of a bat

When a light bulb is connected across the terminals of a battery, the battery delivers 28 W of power to the bulb. A voltage of 12.6 V exists between the terminals of the battery, which has an internal resistance of 0.18 . What is the emf of the battery?
________V

Solution

22 W delivered to the bulb. and 11.4 V is the voltage across the bulb, then with P=VI = 28W, I=P/V = 28/12.6 = 2.22 A

The voltage across the bulb is the same as the voltage across the batterie(with it\'s internal resistance)

The batterie is like ----|--^^^------, the voltage across the battery is the voltage EMF and the voltage of the resistance (plugged from the positive side of the battery)

so the equation is 12.6 - EMF + rI = 0 with r = 0.18 ohm.

EMF = 11.4+rI = 12.6+0.18*2.22 = 12.9996 ~ 13 V.