The rating of the fuse to be used for the cooler and fan can be determined by considering the power requirements of both appliances.

Calculating the Total Power:
To find the total power consumed by the cooler and fan, we need to add their individual power ratings.

Given:
Cooler power rating = 1500 W
Fan power rating = 500 W

Total power = Cooler power + Fan power
= 1500 W + 500 W
= 2000 W

Therefore, the total power consumption of both appliances is 2000 W.

Determining the Fuse Rating:
The fuse rating is used to protect the electrical circuit from overloading. It is important to choose a fuse rating that is slightly higher than the total power consumption of the appliances to ensure their safe operation.

In general, it is recommended to use a fuse with a rating 10-15% higher than the total power consumption. This is because appliances may draw slightly more power during startup or under certain conditions.

Let's calculate the fuse rating using the recommended range:

Fuse rating = Total power consumption x 1.1 (10% higher)
= 2000 W x 1.1
= 2200 W

Therefore, the recommended fuse rating for the cooler and fan is 2200 W.

Choosing the Appropriate Fuse:
Standard fuse ratings are available in specific values. In this case, we need to choose a fuse with a rating equal to or higher than the calculated value. Fuses typically come in standard ratings such as 5A, 10A, 15A, etc.

Since the calculated fuse rating is 2200 W, the nearest standard rating higher than this value is 10A. Therefore, a 10A fuse would be appropriate for this setup.

Conclusion:
For the cooler and fan with power ratings of 1500 W and 500 W respectively, the recommended fuse rating is 2200 W. Since there are no standard fuses available in this exact rating, a 10A fuse can be used as the closest standard rating higher than the calculated value. This fuse will protect the electrical circuit from overloading and ensure the safe operation of the appliances.