how are resistance and power of an appliance connected in parallel with the battery related?
Resistance and power are both qualities to measure current. Resistance is anything that prevents current from flowing such as a light blub. Resistance is measured by Ohm's Law (V=IR) and current in directly proportional to the resistance meaning that when the resistance increases, the current descreases. An appliance would be an example of a resistor because it impedes the current. Power is how much energy the current has put into the circuit. To measure power, the amount of resistance must be considered. The battery supplies the power to the current to the circuit. Power, battery, and resistance all work together to make an appliance run.