A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.

To find the RMS (root mean square) value of the current flowing through a 44 mH inductor connected to a 220 V, 50 Hz AC supply, we need to understand a few important concepts relating to inductors in AC circuits. Let's break this down step by step.

Understanding Inductive Reactance

First, we need to calculate the inductive reactance (X_L) of the inductor. Inductive reactance is a measure of how much the inductor resists the change in current due to its inductance. The formula for inductive reactance is:

X_L = 2πfL

Where:

• f = frequency of the AC supply (in hertz)
• L = inductance (in henries)

Plugging in the Values

For this problem:

• f = 50 Hz
• L = 44 mH = 44 × 10^-3 H = 0.044 H

Now, substituting these values into the formula:

X_L = 2π(50)(0.044) ≈ 14.0 Ω

Calculating RMS Current

With the inductive reactance calculated, we can now find the RMS current (I_rms) using Ohm's Law, which in the context of AC circuits can be expressed as:

I_rms = V_rms / X_L

Where:

• V_rms = RMS voltage of the AC supply (in volts)
• X_L = inductive reactance (in ohms)

Given that the RMS voltage V_rms is 220 V, we can substitute the values into the formula:

I_rms = 220 V / 14.0 Ω ≈ 15.71 A

Final Result

Thus, the RMS value of the current flowing through the circuit is approximately 15.71 A. This means that under the given conditions, the inductor allows this amount of current to flow with respect to the applied AC voltage.

In summary, when dealing with inductors in AC circuits, it is essential to calculate the inductive reactance first, as it plays a crucial role in determining the current based on the voltage applied. The relationship between voltage, inductance, and frequency is vital for understanding how inductors behave in alternating current scenarios.