# Lab 14: Frequency Response of the Series R-L Circuit

## Objectives

• Observe the effect of frequency on the impedance of a series R-L circuit.
• Plot the voltages and current of a series RL circuit versus frequency & interpret them.
• Predict and plot the phase angle of the total impedance versus frequency for a series R-L circuit and relate them to the Phasor voltages.

## Background

#### Series R-L

According to the voltage divider rule (VDR), in a series R-L circuit, the voltage vL (vR) is directly related to the inductive reactance XL (resistive reactance R):

$${v_L} = \frac{{{X_L}}}{Z}{v_{source}}$$ and $${v_R} = \frac{R}{Z}{v_{source}}$$

Where the internal resistance of the inductor is ignored and the total impedance is: $$Z = \sqrt {{R^2} + X_L^2} = \sqrt {{R^2} + {{(2\pi fL)}^2}}$$

Since the inductive reactance XL increases with increasing frequency changes (XL = 2πfL), the voltage drop across the inductor will also increase with frequency. However, the resistive reactance is independent of frequency changes.

The phase angle associated with the impedance Z is also sensitive to the applied frequency: $$\theta = {\tan ^{ - 1}}\frac{{{X_L}}}{R}$$

At very low frequencies the inductive reactance will be small compared to the series resistive element (R >> XL) and the network will be primarily resistive in nature. The result is a phase angle associated with the impedance Z that approaches (V and I in phase). At increasing frequencies, inductive reactance will drown out the resistive element (XL >> R) and the circuit will be primarily inductive, resulting in a phase angle approaching 90° (V leads I by 90°).

## Questions

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