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 root mean square (rms) value of the current flowing through a 44 mH inductor connected to a 220 V, 50 Hz AC supply, we can follow a systematic approach that involves understanding the relationship between voltage, inductance, and current in an AC circuit.

Key Concepts to Consider

In an AC circuit involving an inductor, the inductive reactance (X_L) plays a critical role. Inductive reactance is the opposition that inductors present to AC, and it is given by the formula:

X_L = 2πfL

where:

• f = frequency in hertz (Hz)
• L = inductance in henries (H)

Once we have the inductive reactance, we can use Ohm's law for AC circuits, which states that:

I_rms = V_rms / X_L

where:

• I_rms = rms current in amperes (A)
• V_rms = rms voltage in volts (V)

Step-by-Step Calculation

Now let's go through the calculations step by step:

1. Calculate Inductive Reactance (X_L)

First, we need to convert the inductance from millihenries to henries:

L = 44 mH = 44 × 10^-3 H = 0.044 H

Next, plug in the values into the formula for inductive reactance:

X_L = 2πfL = 2π(50)(0.044)

This calculates to:

X_L ≈ 2π(50)(0.044) ≈ 13.84 Ω

2. Calculate the rms Current (I_rms)

Now we can use Ohm's law to find the rms current:

I_rms = V_rms / X_L

Substituting the known values:

I_rms = 220 V / 13.84 Ω ≈ 15.9 A

Final Result

Thus, the rms value of the current in the circuit is approximately 15.9 A. This value indicates how much current flows in an AC circuit with the given specifications, illustrating the significant impact of inductive reactance in determining current flow.