To find the root mean square (RMS) value of the given alternating current, follow these steps:

The current is represented as:

Here, the time-independent DC component is and the AC component is

Calculate the square of the current, :

Simplifying, we have:

Find the average value :
The average value of cos terms over a period is zero, simplifying our equation to:

This simplifies to:

Calculate the RMS current:
The RMS value is the square root of the mean of the squares of the current:

Thus, the RMS value of the current is 10 Amps.