Both alternating current and direct current are measured in amperes. But how is the ampere defined for an alternating current?

Hint: Understand the difference between AC current and DC current. It is known that AC current depends on direction as an extra factor. Use the above logic, compare it with joules law and arrive at your solution.

Complete answer:
Let us understand the basic difference between AC current and DC current.
In direct current, the flow of electric charge is unidirectional. It is always in steady state in a constant voltage circuit.
Whereas in alternating current, the flow of electric charge is multidirectional and isn’t steady state flow. This means that AC current changes direction with frequency. It is also known that AC current periodically reverses its direction and hence creates an endless sinusoidal wave.
So AC current must be defined in terms of amperes but should be defined in terms of some property which is purely independent of the multidirectional nature of current. We can use Joule’s heating effect which defines current independent of direction. This can be used to define the root mean square value of current.
In DC , current is defined as the ratio between the charge carried or flowing through the circuit in a particular time period.
Hence Root mean square current value of AC is equal to that current in DC. When this current is passed through resistance R, it will produce the same amount of heat in both AC and DC.

Thus current in AC is measured in root mean square value.

Note:
Joule’s heating effect describes the process where the energy of an electric circuit will be converted to heat as it begins to flow through a resistor of resistance R. \[H = {I^2}RT\]