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

Explanation

To define the ampere for alternating current (AC), we can follow these steps:

### Step 1: Understand the Definition of Ampere for Direct Current (DC)
For direct current (DC), the ampere is defined as the flow of one coulomb of charge per second. This is expressed mathematically as:
\[ I = \frac{Q}{T} \]
where \( I \) is the current in amperes, \( Q \) is the charge in coulombs, and \( T \) is the time in seconds. Therefore,
\[ 1 \text{ ampere} = 1 \text{ coulomb/second} \]

### Step 2: Recognize the Nature of Alternating Current (AC)
In alternating current, the direction of the current changes periodically. This means that the current does not flow in a constant direction as it does in DC. Instead, it reverses direction every half cycle.

### Step 3: Identify the Challenge in Defining Ampere for AC
Due to the changing direction of AC, it becomes difficult to define the ampere using the same method as for DC. Since the current alternates, simply counting the charge flow per second does not provide a consistent measure.

### Step 4: Introduce the Concept of Joule Heating
To define the ampere for AC, we can use the concept of Joule heating, which is the heat produced in a resistor due to the flow of current. The power (P) dissipated in a resistor due to current is given by:
\[ P = I^2 R \]
where \( R \) is the resistance. The heating effect is proportional to the square of the current.

### Step 5: Define Ampere for AC
Thus, for alternating current, the ampere is defined in terms of the heating effect it produces in a resistor. Specifically, 1 ampere of AC is defined as the current that produces the same amount of heat in a resistor as 1 ampere of DC would produce under the same conditions.

### Final Definition
In summary, for alternating current, the ampere is defined based on the Joule heating effect, which is proportional to the square of the current:
\[ \text{1 ampere (AC)} = \text{current that produces equivalent heating effect as 1 ampere (DC)} \]

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