In politics Power gets used to implement a decision.
The role of Power becomes most effective when Power does not remain a source of coercion. In-fact after getting legitimized it becomes Authority. Means the stability of Authority depends upon legitimacy.
So in short Authority is a quality or capacity of a person, institution, rule or order which becomes important in defining whether Authority is correct or authentic, so that people can follow the rules and regulation without any hesitation.
Because of the use of Authority official Governmental policies, rules and regulations get accepted in the society. Authority has two main components: Power and Legitimacy.
Legitimacy of a rule or a decision signifies the fact that people reckon the decision as fruitful and in welfare of the society. Thus they are always ready to follow the rule or decision. Demonstration of Power does not become necessary as long as Legitimacy is attached to Power. It only comes out as a symbol. Like a judge with his black gown or a policeman with his uniform. Just like beauty lies in the eyes of beholder, Legitimacy lies in the eyes of beholder.
There is no question, that without Power it will be very difficult to implement the official decision as well as rules, but only by the fear of punishment or by the coercion authority may not prove successful as far as long term benefits are concerned. Infact such a step becomes tyranny and works as a catalyst for the rebellion.
The able use of Power always gets support from legitimacy. Most of the society follows the rules on the basis of legitimacy therefore using Power does not become necessary all the time. No one will follow the rule or a regulation if the legitimacy of that rule is ruined irrespective of the Power of Authority.