LABORATORY 06 · ELECTRICAL & ELECTRONICS ENGINEERING

Verification of Reciprocity and Millman Theorems in Passive and Active Electric Networks

Verify the Reciprocity Theorem by swapping excitation and response ports in a passive bilateral network, and confirm Millman's Theorem in parallel generator topologies. Explore interactive circuit analysis, electronics simulation, and electrical engineering telemetry.

CIRCUIT ANALYSIS · ANALOG · DIGITAL · MACHINES · POWER SYSTEMS · CONTROL & INSTRUMENTATION

Your virtual electrical & electronics engineering laboratory.

TRANSFER OPEN-CIRCUIT VOLTAGE V_2—

INSTRUMENTATION TELEMETRY

Ready to sample with Source Current = 3.0 mA.

Excitation Source Current I_s3.0 mASet Source Current (mA)

Calibrated Bilateral Resistive Ladder Network baseline operating point stabilized at 25.0 °C

Adjust Source Current, then execute electrical instrumentation acquisition.

Electrical telemetry is sampled with calibrated high-precision instruments using 64-bit IEEE 754 precision buffers. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity circuit and power system modeling.

Electrical engineering assumptions and boundary limits

Assumes ideal linear operating conditions without thermal breakdown or non-linear core saturation Calibrated using the Bilateral Resistive Ladder Network under controlled temperature and 64-bit IEEE 754 precision instrumentation buffers. Ordinary least-squares regression yields R² > 0.99999.

Laboratory apparatus & testing equipment.

Reciprocity & Millman Theorems Precision Workstation

Provides regulated excitation, calibrated terminal access, and low-parasitic interconnects for symmetric transfer admittance & multi-branch bus voltage reduction.

True-RMS Digital Multimeter (6.5-digit Keysight / Fluke)

Measures terminal voltages, branch currents, and precision DC/AC parameters with ±0.0035% baseline accuracy.

Dual-Channel Digital Storage Oscilloscope (100 MHz, 1 GSa/s)

Captures time-domain waveforms, phase shifts, transient dynamics, and harmonic spectra for reciprocity & millman theorems.

Regulated Linear DC / AC Variable Power Source

Supplies low-noise, ripple-free voltage and current excitation with adjustable current limiting.

Calibrated Decade Resistance & Component Substitution Box

Provides precision 0.1% tolerance standard passive values to establish calibrated source current conditions.

Four-Terminal Kelvin Lead Wire & BNC Coaxial Cable Set

Minimizes lead resistance, inductive pickup, and ambient EMI interference across all test ports.

FOLLOW THE METHOD

A reason behind every step.

Verify the Reciprocity Theorem by swapping excitation and response ports in a passive bilateral network, and confirm Millman's Theorem in parallel generator topologies. Standardized parameter settings: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 mA.

Visual Inspection & Pre-Flight Zero Tare: Inspect all circuit connections, breadboard jumpers, and terminal blocks. Verify that instrument ground planes are tied to earth and execute zero tare on all digital meters.
Excitation Source & Baseline Calibration: Energize the regulated supply, set baseline operating thresholds, and calibrate the source current using the precision standard reference meter.
Systematic Parameter Variation & Settling: Increment the source current systematically across the designated experimental range (1.0 to 6.0 mA), permitting thermal settling at each setpoint.
Multi-Meter & Oscilloscope Waveform Acquisition: Record the primary output metric (Transfer Open-Circuit Voltage V_2) alongside auxiliary telemetry. Verify waveform symmetry, DC offset, and harmonic integrity on the oscilloscope.
Cross-Validation & Redundant Trial Verification: Execute repeated forward and reverse sweeps to detect hysteresis, thermal drift, or non-linear saturation effects across the device under test (DUT).
Shutdown, De-energization & Data Archival: Reduce source excitation smoothly to zero, de-energize all primary supplies, discharge residual capacitive elements, and export raw telemetry to the data buffer.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into electrical engineering insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Reciprocity & Millman Theorems mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b

V_2 = 0.6500 · I_s

#	Excitation Source Current I_s (mA)	Transfer Open-Circuit Voltage V_2 (V)	Excitation current I_s (mA)	Transfer voltage V_2 (V)

No readings yet. Execute an electrical trial and record it.

CHECK YOUR UNDERSTANDING

Explain what the circuit metrics mean.

Question 1: In the study of Reciprocity & Millman Theorems, the primary dependent variable measured is:

Question 2: The mathematical relationship governing Reciprocity & Millman Theorems is modeled as:

Question 3: The target benchmark parameter derived from regression analysis is:

Question 4: Which instrumentation technique effectively eliminates lead wire resistance error?

THEORY AND ELECTROMAGNETIC CONTEXT

Electrical engineering background & physical principles.

The experimental analysis of verification of reciprocity and millman theorems in passive and active electric networks investigates the electrotechnical behavior of bilateral resistive ladder network. This university laboratory module focuses on symmetric transfer admittance & multi-branch bus voltage reduction, establishing accurate mathematical transfer characteristics across standard operational domains.

V_2 = 0.6500 · I_s

Calibrated using the Bilateral Resistive Ladder Network under controlled temperature and 64-bit IEEE 754 precision instrumentation buffers. Ordinary least-squares regression yields R² > 0.99999.