AC Resistance Measurement Explanation

Introduction

Measuring resistance in an AC circuit involves using Ohm's Law, but the accuracy of the measurement depends on capturing the full current flow. This document explains why measuring current from only one wire in an AC circuit can lead to inaccurate resistance and power calculations, especially when dealing with amplifier setups.

Key Concepts

• Ohm's Law: R = V / I
• Total Current: I_total = V / R
• Power: P = V * I
• Per Wire Current (Balanced Split): I_per_wire = I_total / 2

What Happens When You Clamp One Wire?

In amplifier setups with balanced output, the current is distributed evenly between the positive and negative wires. If you measure current from only one wire, you're capturing only half of the total current flow, which affects calculations:

• Current: The measured current is halved.
• Resistance: Since R = V / I, the resistance is overestimated by a factor of two.
• Power: Since P = V * I, the power is underestimated by 50%.

Example Setup

Consider the following setup:

• Load Resistance: 1 Ω
• Amplifier Voltage: 40 V RMS
• Total Current: I_total = 40 V / 1 Ω = 40 A
• Current Per Wire: I_per_wire = 40 A / 2 = 20 A

Comparison of Measurements

Here's how the calculations differ depending on whether you clamp one wire or both:

• Both Wires Clamped:
  • Current: 40 A
  • Resistance: R = 40 V / 40 A = 1 Ω
  • Power: P = 40 V * 40 A = 1600 W
• One Wire Clamped:
  • Current: 20 A
  • Resistance: R = 40 V / 20 A = 2 Ω
  • Power: P = 40 V * 20 A = 800 W

Key Takeaways

Clamping only one wire leads to inaccurate results because it only measures half the total current flow. Always measure the full current by clamping both wires to ensure accurate calculations for resistance and power.

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