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AC circuit with inductance and resistance

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Introduction to the AC Circuit with Inductance and Resistance

An AC circuit containing inductance only is a circuit that consists of only the inductor as a component. We use such inductors in the AC circuit as filters. They are known to store energy in the form of magnetic energy and hence are known for reducing fluctuation during the flow of electric current.

This experiment is a foundational exercise in medical physics laboratories, helping students connect electrical theory to the instrumentation used throughout clinical practice — from diagnostic imaging to patient monitoring equipment.

Aim of The AC circuit with inductance and resistance

The aim of the AC circuit with inductance and resistance experiment is : measuring the inductance of the coil.

Tools of The Experiment

·       Low voltage A.C. source.

·       fixed inductance.

·       Resistance box.

·       A.C. ammeter.

Steps And Method of The Experiment

1-Feed the low-voltage output into the circuit connected as shown in the diagram.

2-Vary R and record the circuit current I as read on the A.C. ammeter at each stage.

3-Tabulate the readings.

4-plot the graph between Z2 and R2.

5-Find the slope.

Parameters, Theory And Final Law of The experiment

Parameters:

XL: is the inductive reactance of the coil (Ω)
L: inductance of the coil (H)
Z2: Total impedance (Ω)
R: Resistance (Ω)
I: Current (A)
V: Voltage (V)

As current flows through the inductor, it generates a magnetic field that opposes changes in current — this opposition is the inductive reactance, XL. Since XL depends on frequency (XL = 2πfL), the impedance Z of the circuit varies with both the fixed inductance and the resistance introduced by the resistance box.

By systematically varying R and measuring the resulting current, students can isolate the inductive component from the resistive one, giving a practical method for determining an unknown inductance without needing specialized measuring equipment.

Theory

A O
Z = VI
I = VZ = V R2 + x2
Z2 = R2 + XL2

Where XL is the inductive reactance of the coil. A graph of Z² against R² yields a straight line — the intercept (OA) gives the value of X²L.


Thus
XL2 = OA = (2πfL)2

And from this, the inductance (L) of the coil can be determined:

L = OA f
Final Law
Z2 = R2 + XL2

Table of readings for the AC circuit with inductance and resistance (V = 6 Volt).

V = 6 Volt
R/Ω I/A Z = V/I
0
10
30
·
·

Medical Application

Understanding the AC circuit with inductance and resistance has direct clinical relevance in the following areas:

  • Portable diagnostics
    Handheld blood analyzers, glucose monitors, and blood pressure devices rely on switching regulators built around inductors to deliver high efficiency even at low load currents, extending battery life in point-of-care settings.
  • MRI signal circuits — Capacitor–inductor series combinations tune and filter the radiofrequency circuitry at the core of MRI systems, shaping the signal for accurate imaging.
  • High-voltage imaging & laser systems — X-ray machines and laser systems pair inductance with capacitors and resistors in high-voltage circuits to control power delivery precisely and safely.

    Together, these examples show how a simple inductance-resistance circuit underlies much of the electronic infrastructure powering modern diagnostic and therapeutic medical devices.

Lab Tips

Common Mistakes to Avoid in AC circuit with inductance and resistance experiment

  • Forgetting to record the resistance box’s own internal resistance, which adds a small but measurable offset to R.
  • Taking readings too quickly without letting the ammeter stabilize, especially at low current values.
  • Plotting Z against R instead of Z² against R² — the linear relationship only holds in squared form.

Download The Data Sheet

Frequently Asked Questions About the AC Circuit with Inductance and Resistance

What is inductive reactance (XL)?

The opposition an inductor presents to alternating current, caused by the changing magnetic field it generates. It depends on both the coil's inductance and the frequency of the AC source.

Why plot Z² against R² instead of Z against R?

Squaring linearizes the relationship — since Z² = R² + XL², plotting these two gives a straight line whose intercept directly yields XL², making the inductance easy to extract graphically.

What affects the accuracy of this experiment?

Contact resistance in the resistance box, ammeter calibration, and stray capacitance in the leads can all introduce small errors into the readings.