- #1

Jason-Li

- 119

- 14

## Homework Statement

An ac voltage, comprises of a fundamental voltage of 100 Vrms at a frequency of 120 Hz, a 3rd harmonic which is 20% of the fundamental, a

5th harmonic which is 10% of the fundamental and at a phase angle of

1.2 radians lagging.

(i) Write down an expression for the voltage waveform.

(ii) Sketch the waveforms of the harmonic components.

(iii) Determine the voltage at 20 ms.

(iv) Given an ideal V = 100 V rms, what is the percentage error at 20 ms?

## The Attempt at a Solution

(i)

A 1Hz = 2π rads^-1 so:

Fundamental = 120Hz = 240π, 3rd = 360Hz = 720ω & 5th = 600Hz = 1200π lagging by 1.2 radians

Vrms = 100V so Vmax or A = 100 * √2 = 141.421V

3rd = 0.2 * 141.421 = 28.2842V

5th = 0.1 * 141.421 = 14.1421V

so written as one expression:

141.421sin(240πt)+28.284*sin(720πt)+14.1421*sin(1200πt-1.2)

(ii) Attached at bottom

(iii) where t = 20ms or 0.02s

141.421sin(240πt)+28.284*sin(720πt)+14.1421*sin(1200πt-1.2)

141.421sin(240π*0.02)+28.284*sin(720π*0.02)+14.1421*sin(1200*π*0.02-1.2)

=96.844V

(iv) Ideal Vrms = 100V, V at 20ms = 96.844V

As 96.844V was found from 'max' value,

Percentage error = (1-(V@20ms/V)*100

= (1-(96.844/141.421)*100

=(1-0.6848)*100

= 31.5%

Can anyone confirm if I am along the right lines? just seems like an excessive percentage error and unsure if I should use max values or RMS values for (iv)