Theory- 13 :- Inductive reactance, measuring inductance and inductive reactance. Meaning of lead, lag. Effect of inductor on power factor. Frequency dependence of inductive reactance.

Inductive Reactance and Inductance

What is Inductance (L)?

Think of an inductor as being "electrically heavy" or "stubborn."

• Analogy: Imagine a very heavy water wheel in a stream. When you first open the gate to let water flow (like turning on a circuit), the heavy wheel takes a moment to get up to speed. It resists the change from being stationary to moving. If you then suddenly close the gate, the wheel's momentum will try to keep it spinning for a bit. It resists the change from moving to stationary.

This property of resisting a change in current is called inductance (L). It's caused by the magnetic field that the current creates around the inductor coil. The coil doesn't like it when its magnetic field changes, so it pushes back against the current that's causing the change.

• Unit: We measure this "electrical heaviness" in Henries (H). A higher Henry value means a more "stubborn" inductor.

What is Inductive Reactance (XL​)?

Now, imagine that instead of a steady stream, you are sending waves of water (like alternating current - AC). The water is constantly pushing forward, then pulling back, over and over.

Because the heavy water wheel (our inductor) hates change, it's going to fight this constant back-and-forth motion a lot! This continuous opposition to AC is called inductive reactance (XL). It's like a special kind of resistance that only shows up for AC.

The formula for this is:    

Let's break that down:

• : This is the Inductive Reactance, the opposition we're talking about. It's measured in Ohms (Ω), just like regular resistance.

• : This is the Frequency of the AC. How fast is the current changing direction? The faster you try to move the heavy water wheel back and forth, the more it will fight you. So, higher frequency means higher reactance.

• : This is the Inductance. A heavier water wheel will fight you more than a lighter one. So, higher inductance means higher reactance.

• : This is just a constant number (≈6.28 ) that makes the math work out correctly, related to the circular nature of AC waves.

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Meaning of Lead and Lag

This describes the timing relationship between AC Voltage and AC Current.

• Analogy: Imagine you are walking a very large, lazy dog on a leash. You are the Voltage (the force) and the dog is the Current (the flow/movement).

  • When you start walking forward, the dog takes a second to react. For a moment, you are moving but the dog isn't.

  • When you stop, the dog plods along for another step before realizing you've stopped.

  • No matter what you do, the dog is always a moment behind you.

This is exactly what happens in an inductive circuit. The inductor's "heaviness" causes the current to take a moment to react to the changes in voltage.

• We say the Current LAGS behind the Voltage.

• In a perfect inductor, this lag is exactly one-quarter of a cycle, which we measure as 90 degrees (90∘).

As you can see in the diagram, the Voltage (blue) wave starts and peaks before the Current (red) wave does. The current is lagging.

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Measuring Inductance and Inductive Reactance

Measuring Inductance (L)

The easiest and most modern way is to use a special tool called an LCR Meter. You simply connect the inductor to the meter's terminals, and it directly tells you its inductance in Henries (H), millihenries (mH), or microhenries (µH). It's the most accurate method.

Calculating Inductive Reactance (XL​)

You can't measure reactance directly with a multimeter, but you can find it in two ways:

Method 1: The Practical Test (Using Ohm's Law)

This is how you'd find it if you have an unknown inductor.

1. Set up a circuit: Connect your inductor to an AC power source with a known voltage (e.g., a signal generator or a transformer).

2. Measure Voltage: Use a multimeter set to AC VOLTS to measure the voltage (V) directly across the inductor.

3. Measure Current: Set the multimeter to AC AMPS. You must place the meter in series with the inductor (like a link in a chain) to measure the current (I) flowing through it.

4. Calculate: Use Ohm's law. The opposition (XL​) is simply the voltage divided by the current. 

   
   
   
   

   Example: If you measure 24 Volts across the inductor and 0.2 Amps flowing through it, the reactance is 24V÷0.2A=120 Ω.

Method 2: The Formula Way

This is what you do if you already know the inductor's value and the circuit's frequency.

1. Find the values: Look at the component to find its Inductance (L) and know the frequency (f) of your circuit (e.g., for standard wall power in India,  $f=50$ Hz).

2. Calculate: Plug the numbers into the formula.  

   
   
   
   

   Example: You have a 150 mH (which is 0.15 H) inductor in a 50 Hz circuit.

   XL​=2×3.14159×50 Hz×0.15 H≈47.1 Ω

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Effect of an Inductor on Power Factor

What is Power Factor? The Beer Analogy! 🍺

Inductor's Effect

Because inductors cause the current to lag the voltage (creating that "sideways pull"), they generate reactive power. This means the power company has to supply more total power (the horse must pull harder) to get the same amount of useful work done (moving the cart forward).

Therefore, an inductor lowers the power factor and makes it a lagging power factor. This is inefficient and can lead to higher electricity bills.

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Frequency Dependence of Inductive Reactance