Which of the following equations is the correct definition of the reactance of an indicator L?

1. Analyze the question

The question asks for the definition of the reactance ($X_L$) of an inductor in an A.C. circuit. Reactance is essentially the "opposition" to the flow of alternating current caused by an inductor, measured in Ohms ($\Omega$).

2. Explain the concept

In an A.C. circuit, Ohm's Law applies to components like resistors, capacitors, and inductors. For an inductor, the relationship between the voltage across it ($V_L$) and the current flowing through it ($I_L$) is governed by the inductive reactance ($X_L$).

The formula for Ohm's Law in an A.C. circuit is:

Where $Z$ is the impedance (or reactance, in the case of a pure inductor). Therefore:

When dealing with A.C. signals, we often use the peak values (amplitudes) of the voltage ($V_0$) and the current ($I_0$). Thus, the inductive reactance is defined as the ratio of the amplitude of the voltage to the amplitude of the current.

3. Show the solution

• Step 1: Identify the relationship between voltage and current for an inductor: $V_L = I_L \times X_L$.
• Step 2: Rearrange the formula to solve for reactance ($X_L$): $X_L = \frac{V_L}{I_L}$.
• Step 3: Apply this to the amplitudes (peak values): $X_L = \frac{\text{Amplitude of Voltage}}{\text{Amplitude of Current}}$.
• Step 4: Compare this result with the given options. Option A matches this derivation perfectly.

4. Identify the answer

The correct definition is the ratio of the amplitude of the voltage to the amplitude of the current.

Correct Option: A

5. Tip

Remember the acronym "V-I-R" (or in this case, V-I-X). Whenever you are asked for resistance, reactance, or impedance, it is almost always Voltage divided by Current. If you ever forget the formula, just look at the units: Resistance/Reactance is in Ohms ($\Omega$), Voltage is in Volts ($V$), and Current is in Amperes ($A$). Since $V = I \times R$, then $R = V/I$.