A coil has an inductive reactance (XL) of 188.4 ohms and an internal resistance (R) of 82 ohms. If the coil is connected to a 120-volt, 60-hertz source, what will be the current through this series RL circuit?

To determine the current through a series RL circuit, you first need to find the total impedance (Z) of the circuit. In a series RL circuit, the impedance is calculated using the formula:

Z = √(R² + XL²)

where R is the internal resistance and XL is the inductive reactance.

Here, R is 82 ohms and XL is 188.4 ohms. Plugging these values into the formula gives:

Z = √(82² + 188.4²)

Z = √(6724 + 35593.76)

Z = √(42317.76)

Z ≈ 205.7 ohms

Once you have the total impedance, you can find the current (I) flowing through the circuit using Ohm's Law:

I = V / Z

where V is the voltage across the circuit. In this case, the voltage is 120 volts. Substituting the values gives:

I = 120 / 205.7

I ≈ 0.58 A

This calculation confirms that the current flowing through the coil when connected to the 120-volt, 60-hertz source is indeed approximately 0.58 A. This demonstrates the importance