Question

what are harmonics? Explain with a diagram.​

Answer 1

Ꭺɳsωεɾ:-

A ʜᴀʀᴍᴏɴɪᴄ ɪs ᴀɴʏ ᴍᴇᴍʙᴇʀ ᴏғ ᴛʜᴇ ʜᴀʀᴍᴏɴɪᴄ sᴇʀɪᴇs. Tʜᴇ ᴛᴇʀᴍ ɪs ᴇᴍᴘʟᴏʏᴇᴅ ɪɴ ᴠᴀʀɪᴏᴜs ᴅɪsᴄɪᴘʟɪɴᴇs, ɪɴᴄʟᴜᴅɪɴɢ ᴍᴜsɪᴄ, ᴘʜʏsɪᴄs, ᴀᴄᴏᴜsᴛɪᴄs, ᴇʟᴇᴄᴛʀᴏɴɪᴄ ᴘᴏᴡᴇʀ ᴛʀᴀɴsᴍɪssɪᴏɴ, ʀᴀᴅɪᴏ ᴛᴇᴄʜɴᴏʟᴏɢʏ, ᴀɴᴅ ᴏᴛʜᴇʀ ғɪᴇʟᴅs. Iᴛ ɪs ᴛʏᴘɪᴄᴀʟʟʏ ᴀᴘᴘʟɪᴇᴅ ᴛᴏ ʀᴇᴘᴇᴀᴛɪɴɢ sɪɢɴᴀʟs, sᴜᴄʜ ᴀs sɪɴᴜsᴏɪᴅᴀʟ ᴡᴀᴠᴇs. 

Tʜᴇ Fᴏᴜʀɪᴇʀ ᴛʜᴇᴏʀᴇᴍ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴀʟʟ ɴᴏɴ-sɪɴᴜsᴏɪᴅᴀʟ ᴘᴇʀɪᴏᴅɪᴄ ғᴜɴᴄᴛɪᴏɴs ᴄᴀɴ ʙᴇ ʀᴇᴘʀᴇsᴇɴᴛᴇᴅ ᴀs ᴛʜᴇ sᴜᴍ ᴏғ ᴛᴇʀᴍs (ɪ.ᴇ. ᴀ sᴇʀɪᴇs) ᴍᴀᴅᴇ ᴜᴘ ᴏғ:

• A sɪɴᴜsᴏɪᴅᴀʟ ᴛᴇʀᴍ ᴀᴛ ᴛʜᴇ ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ғʀᴇϙᴜᴇɴᴄʏ,

• Sɪɴᴜsᴏɪᴅᴀʟ ᴛᴇʀᴍs (ʜᴀʀᴍᴏɴɪᴄs) ᴡʜᴏsᴇ ғʀᴇϙᴜᴇɴᴄɪᴇs ᴀʀᴇ ᴡʜᴏʟᴇ ᴍᴜʟᴛɪᴘʟᴇs ᴏғ ᴛʜᴇ ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ғʀᴇϙᴜᴇɴᴄʏ,

• A DC ᴄᴏᴍᴘᴏɴᴇɴᴛ, ᴡʜᴇʀᴇ ᴀᴘᴘʟɪᴄᴀʙʟᴇ.

Current or voltage THD

For current harmonics the equation is:

${\displaystyle THD_{i}={\sqrt {\sum _{h=2}^{h=H}\left({\frac {I_{h}}{I_{1}}}\right)^{2}}}}{\displaystyle THD_{i}={\sqrt {\sum _{h=2}^{h=H}\left({\frac {I_{h}}{I_{1}}}\right)^{2}}}}$

By introducing the total r.m.s value of the current:

${\displaystyle I_{rms}={\sqrt {\sum _{h=1}^{h=H}I_{h}^{2}}}}{\displaystyle I_{rms}={\sqrt {\sum _{h=1}^{h=H}I_{h}^{2}}}}$

we obtain the following relation:

${\displaystyle THD_{i}={\sqrt {\left({\frac {I_{rms}}{I_{1}}}\right)^{2}-1}}}{\displaystyle THD_{i}={\sqrt {\left({\frac {I_{rms}}{I_{1}}}\right)^{2}-1}}}$

equivalent to:

${\displaystyle I_{rms}=I_{1}{\sqrt {1+THD_{i}^{2}}}}{\displaystyle I_{rms}=I_{1}{\sqrt {1+THD_{i}^{2}}}}$

Example: for THDi = 40%, we get:

${\displaystyle I_{rms}=I_{1}{\sqrt {1+\left(0.4\right)^{2}}}=I_{1}{\sqrt {1+0.16}}\approx I_{1}\times 1.08}{\displaystyle I_{rms}=I_{1}{\sqrt {1+\left(0.4\right)^{2}}}=I_{1}{\sqrt {1+0.16}}\approx I_{1}\times 1.08}$

For voltage harmonics, the equation is:

${\displaystyle THD_{u}={\sqrt {\sum _{h=2}^{h=H}\left({\frac {U_{h}}{U_{1}}}\right)^{2}}}}{\displaystyle THD_{u}={\sqrt {\sum _{h=2}^{h=H}\left({\frac {U_{h}}{U_{1}}}\right)^{2}}}}$

Answer 2

Answer:

Harmonics are unwanted higher frequencies which superimposed on the fundamental waveform creating a distorted wave pattern. In an AC circuit, a resistance behaves in exactly the same way as it does in a DC circuit. That is, the current flowing through the resistance is proportional to the voltage across it.