Lab 4

ENSC 220 Lab 4: First-Order Circuits

Names / IDs / Bench

• Kian Bellinger (301554307)
• Tyler Lee (301560642)
• Kavahn Ahluwalia (301581033)
• Bench #: 2

1. Equipment & Setup

• Wire: $n=161$ turns; diameter $d=0.78\text{ in}$; length $l=3.346\text{ in}$
• Resistors:
  • $R_{RL}=98.31\Omega$
  • $R_{RC}=9.898\text{k}\Omega$
• LCR bridge (1 kHz), oscilloscope, square-wave generator, DMM.

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3. Theory & Calculations

3.1 Inductor via Wheeler’s Formula

Inductance of a single-layer air-core coil:

$$L_{\text{calc}}=\frac{n^2{d}^2}{18d+40l}(\mu \text{H})$$

Substitute $n=161$, $d=0.78\text{ in}$, $l=3.346\text{ in}$:

$$L_{\text{calc}}=\frac{161^2\times 0.78^2}{18\times 0.78+40\times 3.346}\approx 106.642\mu \text{H}$$

3.2 RL Step Response

$$L_{\tau }=R_{RL}{\tau }_{RL}.$$

Measured ${\tau }_{RL}=596\text{ ns}$, $R_{RL}=98.31\Omega$:

$$L_{\tau }=98.31\times 596\times 10^{-9}\approx 58.59\mu \text{H}$$

3.3 RC Step Response

$$C_{\tau }=\frac{{\tau }_{RC}}{R_{RC}}.$$

Measured ${\tau }_{RC}=9\text{ μs}$, $R_{RC}=9.898\text{k}\Omega$:

$$C_{\tau }=\frac{9\times 10^{-6}}{9.898\times 10^3}\approx 0.91\text{nF}$$

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4. Results

Quantity	Method	Value
$L_{\text{calc}}$	Wheeler’s formula	106.642 μH
$L_{\text{LCR}}$	LCR bridge	91.8 μH
$L_{\tau }$	RL time constant	58.59 μH
$C_{\text{LCR}}$	LCR bridge	1.02 nF
$C_{\tau }$	RC time constant	0.91 nF

• Inductor:
  • Formula vs. LCR: –14%
  • Formula vs. τ: –43%
• Capacitor:
  • Bridge vs. τ: –11%