Deno sanex

21/01/2025

𝕎𝕙𝕒𝕥 𝕀𝕤 𝕥𝕙𝕖 𝔻𝕚𝕗𝕗𝕖𝕣𝕖𝕟𝕔𝕖 𝔹𝕖𝕥𝕨𝕖𝕖𝕟 𝕊𝕖𝕟𝕤𝕠𝕣 𝕒𝕟𝕕 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣? . 𝕊𝕖𝕟𝕤𝕠𝕣𝕤 𝕒𝕟𝕕 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤 𝕒𝕣𝕖 𝕗𝕦𝕟𝕕𝕒𝕞𝕖𝕟𝕥𝕒𝕝 𝕔𝕠𝕞𝕡𝕠𝕟𝕖𝕟𝕥𝕤 𝕠𝕗 𝕞𝕠𝕕𝕖𝕣𝕟 𝕥𝕖𝕔𝕙𝕟𝕠𝕝𝕠𝕘𝕪, 𝕡𝕒𝕣𝕥𝕚𝕔𝕦𝕝𝕒𝕣𝕝𝕪 𝕚𝕟 𝕗𝕚𝕖𝕝𝕕𝕤 𝕝𝕚𝕜𝕖 𝕒𝕦𝕥𝕠𝕞𝕒𝕥𝕚𝕠𝕟, 𝕣𝕠𝕓𝕠𝕥𝕚𝕔𝕤, 𝕒𝕟𝕕 𝕀𝕠𝕋 (𝕀𝕟𝕥𝕖𝕣𝕟𝕖𝕥 𝕠𝕗 𝕋𝕙𝕚𝕟𝕘𝕤). 𝔻𝕖𝕤𝕡𝕚𝕥𝕖 𝕠𝕗𝕥𝕖𝕟 𝕓𝕖𝕚𝕟𝕘 𝕞𝕖𝕟𝕥𝕚𝕠𝕟𝕖𝕕 𝕥𝕠𝕘𝕖𝕥𝕙𝕖𝕣, 𝕥𝕙𝕖𝕪 𝕡𝕖𝕣𝕗𝕠𝕣𝕞 𝕕𝕚𝕤𝕥𝕚𝕟𝕔𝕥 𝕪𝕖𝕥 𝕔𝕠𝕞𝕡𝕝𝕖𝕞𝕖𝕟𝕥𝕒𝕣𝕪 𝕣𝕠𝕝𝕖𝕤. 𝕋𝕙𝕚𝕤 𝕒𝕣𝕥𝕚𝕔𝕝𝕖 𝕨𝕚𝕝𝕝 𝕖𝕩𝕡𝕝𝕠𝕣𝕖 𝕥𝕙𝕖 𝕕𝕚𝕗𝕗𝕖𝕣𝕖𝕟𝕔𝕖 𝕓𝕖𝕥𝕨𝕖𝕖𝕟 𝕤𝕖𝕟𝕤𝕠𝕣 𝕒𝕟𝕕 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣, 𝕕𝕖𝕝𝕧𝕚𝕟𝕘 𝕚𝕟𝕥𝕠 𝕥𝕙𝕖𝕚𝕣 𝕕𝕖𝕗𝕚𝕟𝕚𝕥𝕚𝕠𝕟𝕤, 𝕗𝕦𝕟𝕔𝕥𝕚𝕠𝕟𝕒𝕝𝕚𝕥𝕚𝕖𝕤, 𝕒𝕟𝕕 𝕣𝕖𝕒𝕝-𝕨𝕠𝕣𝕝𝕕 𝕒𝕡𝕡𝕝𝕚𝕔𝕒𝕥𝕚𝕠𝕟𝕤.

𝔻𝕚𝕗𝕗𝕖𝕣𝕖𝕟𝕔𝕖-𝔹𝕖𝕥𝕨𝕖𝕖𝕟-𝕊𝕖𝕟𝕤𝕠𝕣-𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣
𝔻𝕚𝕗𝕗𝕖𝕣𝕖𝕟𝕔𝕖-𝔹𝕖𝕥𝕨𝕖𝕖𝕟-𝕊𝕖𝕟𝕤𝕠𝕣-𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣
𝕎𝕙𝕒𝕥 𝔸𝕣𝕖 𝕊𝕖𝕟𝕤𝕠𝕣𝕤?
𝕊𝕖𝕟𝕤𝕠𝕣𝕤 𝕒𝕣𝕖 𝕕𝕖𝕧𝕚𝕔𝕖𝕤 𝕥𝕙𝕒𝕥 𝕕𝕖𝕥𝕖𝕔𝕥 𝕒𝕟𝕕 𝕣𝕖𝕤𝕡𝕠𝕟𝕕 𝕥𝕠 𝕔𝕙𝕒𝕟𝕘𝕖𝕤 𝕚𝕟 𝕥𝕙𝕖𝕚𝕣 𝕖𝕟𝕧𝕚𝕣𝕠𝕟𝕞𝕖𝕟𝕥. 𝕋𝕙𝕖𝕪 𝕞𝕖𝕒𝕤𝕦𝕣𝕖 𝕡𝕙𝕪𝕤𝕚𝕔𝕒𝕝 𝕡𝕙𝕖𝕟𝕠𝕞𝕖𝕟𝕒 𝕝𝕚𝕜𝕖 𝕥𝕖𝕞𝕡𝕖𝕣𝕒𝕥𝕦𝕣𝕖, 𝕝𝕚𝕘𝕙𝕥, 𝕡𝕣𝕖𝕤𝕤𝕦𝕣𝕖, 𝕠𝕣 𝕞𝕠𝕥𝕚𝕠𝕟 𝕒𝕟𝕕 𝕔𝕠𝕟𝕧𝕖𝕣𝕥 𝕥𝕙𝕖𝕤𝕖 𝕚𝕟𝕥𝕠 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝 𝕤𝕚𝕘𝕟𝕒𝕝𝕤 𝕗𝕠𝕣 𝕒𝕟𝕒𝕝𝕪𝕤𝕚𝕤.

𝕎𝕙𝕒𝕥-𝕚𝕤-𝔼𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝-𝕊𝕖𝕟𝕤𝕠𝕣
𝕎𝕙𝕒𝕥-𝕚𝕤-𝔼𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝-𝕊𝕖𝕟𝕤𝕠𝕣
𝕋𝕙𝕖𝕣𝕖 𝕒𝕣𝕖 𝕕𝕚𝕗𝕗𝕖𝕣𝕖𝕟𝕥 𝕥𝕪𝕡𝕖𝕤 𝕠𝕗 𝕤𝕖𝕟𝕤𝕠𝕣𝕤 𝕒𝕧𝕒𝕚𝕝𝕒𝕓𝕝𝕖, 𝔸 𝕗𝕖𝕨 𝕖𝕩𝕒𝕞𝕡𝕝𝕖𝕤 𝕠𝕗 𝕤𝕖𝕟𝕤𝕠𝕣𝕤 𝕒𝕣𝕖 𝕥𝕖𝕞𝕡𝕖𝕣𝕒𝕥𝕦𝕣𝕖, 𝕦𝕝𝕥𝕣𝕒𝕤𝕠𝕟𝕚𝕔, 𝕡𝕣𝕖𝕤𝕤𝕦𝕣𝕖 𝕒𝕟𝕕 𝕡𝕠𝕤𝕚𝕥𝕚𝕠𝕟 𝕤𝕖𝕟𝕤𝕠𝕣, 𝕖𝕥𝕔. 𝔸𝕤 𝕥𝕙𝕖𝕚𝕣 𝕟𝕒𝕞𝕖 𝕤𝕦𝕘𝕘𝕖𝕤𝕥𝕤, 𝕥𝕙𝕖𝕪 𝕒𝕣𝕖 𝕦𝕤𝕖𝕕 𝕗𝕠𝕣 𝕤𝕖𝕟𝕤𝕚𝕟𝕘 𝕒𝕟𝕕 𝕞𝕖𝕒𝕤𝕦𝕣𝕚𝕟𝕘 𝕥𝕙𝕖 𝕣𝕖𝕤𝕡𝕖𝕔𝕥𝕚𝕧𝕖 𝕢𝕦𝕒𝕟𝕥𝕚𝕥𝕚𝕖𝕤.

ℝ𝕖𝕒𝕕 𝕄𝕠𝕣𝕖 : 𝕎𝕙𝕒𝕥 𝕚𝕤 𝕒 𝕋𝕒𝕔𝕥𝕚𝕝𝕖 𝕊𝕖𝕟𝕤𝕠𝕣?

𝔸 𝕤𝕖𝕟𝕤𝕠𝕣 𝕨𝕠𝕣𝕜𝕤 𝕓𝕪 𝕤𝕖𝕟𝕤𝕚𝕟𝕘 𝕥𝕙𝕖 𝕢𝕦𝕒𝕟𝕥𝕚𝕥𝕪 𝕦𝕤𝕚𝕟𝕘 𝕒 𝕤𝕡𝕖𝕔𝕚𝕒𝕝 𝕤𝕖𝕟𝕤𝕚𝕟𝕘 𝕖𝕝𝕖𝕞𝕖𝕟𝕥. 𝔼𝕒𝕔𝕙 𝕤𝕖𝕟𝕤𝕠𝕣 𝕙𝕒𝕤 𝕒 𝕕𝕚𝕗𝕗𝕖𝕣𝕖𝕟𝕥 𝕨𝕠𝕣𝕜𝕚𝕟𝕘 𝕡𝕣𝕚𝕟𝕔𝕚𝕡𝕝𝕖 𝕤𝕦𝕔𝕙 𝕒𝕤 𝕖𝕝𝕖𝕔𝕥𝕣𝕠𝕞𝕒𝕘𝕟𝕖𝕥𝕚𝕔 𝕤𝕖𝕟𝕤𝕠𝕣, 𝕔𝕒𝕡𝕒𝕔𝕚𝕥𝕠𝕣 𝕤𝕖𝕟𝕤𝕠𝕣, 𝕣𝕖𝕤𝕚𝕤𝕥𝕚𝕧𝕖 𝕤𝕖𝕟𝕤𝕠𝕣, 𝕖𝕥𝕔. 𝔾𝕖𝕟𝕖𝕣𝕒𝕝𝕝𝕪, 𝕥𝕙𝕖𝕪 𝕤𝕖𝕟𝕤𝕖 𝕥𝕙𝕖 𝕔𝕠𝕣𝕣𝕖𝕤𝕡𝕠𝕟𝕕𝕚𝕟𝕘 𝕒𝕥𝕥𝕣𝕚𝕓𝕦𝕥𝕖 𝕗𝕣𝕠𝕞 𝕥𝕙𝕖 𝕖𝕟𝕧𝕚𝕣𝕠𝕟𝕞𝕖𝕟𝕥 𝕒𝕟𝕕 𝕔𝕠𝕟𝕧𝕖𝕣𝕥 𝕚𝕥 𝕚𝕟𝕥𝕠 𝕒𝕟 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝 𝕤𝕚𝕘𝕟𝕒𝕝 𝕠𝕗 𝕡𝕣𝕠𝕡𝕠𝕣𝕥𝕚𝕠𝕟𝕒𝕝 𝕞𝕒𝕘𝕟𝕚𝕥𝕦𝕕𝕖.

𝔸 𝕤𝕖𝕟𝕤𝕠𝕣 𝕔𝕒𝕟 𝕖𝕚𝕥𝕙𝕖𝕣 𝕓𝕖 𝕒𝕔𝕥𝕚𝕧𝕖 𝕠𝕣 𝕡𝕒𝕤𝕤𝕚𝕧𝕖. 𝔸 𝕡𝕒𝕤𝕤𝕚𝕧𝕖 𝕤𝕖𝕟𝕤𝕠𝕣 𝕕𝕠𝕖𝕤 𝕟𝕠𝕥 𝕣𝕖𝕢𝕦𝕚𝕣𝕖 𝕒𝕟 𝕖𝕩𝕥𝕣𝕒 𝕡𝕠𝕨𝕖𝕣 𝕤𝕠𝕦𝕣𝕔𝕖 𝕥𝕠 𝕠𝕡𝕖𝕣𝕒𝕥𝕖 𝕨𝕙𝕚𝕝𝕖 𝕒 𝕡𝕒𝕤𝕤𝕚𝕧𝕖 𝕤𝕖𝕟𝕤𝕠𝕣 𝕣𝕖𝕢𝕦𝕚𝕣𝕖𝕤 𝕒𝕟 𝕖𝕩𝕥𝕣𝕒 𝕡𝕠𝕨𝕖𝕣 𝕤𝕠𝕦𝕣𝕔𝕖. 𝔸 𝕡𝕚𝕖𝕫𝕠𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔 𝕤𝕖𝕟𝕤𝕠𝕣 𝕚𝕤 𝕒𝕟 𝕒𝕔𝕥𝕚𝕧𝕖 𝕤𝕖𝕟𝕤𝕠𝕣 𝕥𝕙𝕒𝕥 𝕔𝕠𝕟𝕧𝕖𝕣𝕥𝕤 𝕡𝕣𝕖𝕤𝕤𝕦𝕣𝕖 𝕚𝕟𝕥𝕠 𝕒𝕟 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝 𝕤𝕚𝕘𝕟𝕒𝕝. 𝔸𝕟 𝕖𝕩𝕒𝕞𝕡𝕝𝕖 𝕠𝕗 𝕒 𝕡𝕒𝕤𝕤𝕚𝕧𝕖 𝕤𝕖𝕟𝕤𝕠𝕣 𝕚𝕤 𝕒 𝕡𝕠𝕥𝕖𝕟𝕥𝕚𝕠𝕞𝕖𝕥𝕖𝕣 𝕨𝕙𝕠𝕤𝕖 𝕣𝕖𝕤𝕚𝕤𝕥𝕒𝕟𝕔𝕖 𝕔𝕙𝕒𝕟𝕘𝕖𝕤 𝕨𝕚𝕥𝕙 𝕥𝕙𝕖 𝕡𝕠𝕤𝕚𝕥𝕚𝕠𝕟 𝕓𝕦𝕥 𝕚𝕟 𝕠𝕣𝕕𝕖𝕣 𝕥𝕠 𝕔𝕠𝕟𝕧𝕖𝕣𝕥 𝕚𝕥 𝕚𝕟𝕥𝕠 𝕒𝕟 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝 𝕤𝕚𝕘𝕟𝕒𝕝, 𝕚𝕥 𝕣𝕖𝕢𝕦𝕚𝕣𝕖𝕤 𝕖𝕩𝕥𝕣𝕒 𝕡𝕠𝕨𝕖𝕣 𝕤𝕠𝕦𝕣𝕔𝕖.

ℍ𝕠𝕨 𝕊𝕖𝕟𝕤𝕠𝕣𝕤 𝕎𝕠𝕣𝕜
𝔸 𝕤𝕖𝕟𝕤𝕠𝕣 𝕘𝕒𝕥𝕙𝕖𝕣𝕤 𝕕𝕒𝕥𝕒 𝕗𝕣𝕠𝕞 𝕚𝕥𝕤 𝕤𝕦𝕣𝕣𝕠𝕦𝕟𝕕𝕚𝕟𝕘𝕤.
𝕋𝕙𝕖 𝕕𝕒𝕥𝕒 𝕚𝕤 𝕔𝕠𝕟𝕧𝕖𝕣𝕥𝕖𝕕 𝕚𝕟𝕥𝕠 𝕒𝕟 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝 𝕤𝕚𝕘𝕟𝕒𝕝.
𝕋𝕙𝕖 𝕤𝕚𝕘𝕟𝕒𝕝 𝕚𝕤 𝕥𝕣𝕒𝕟𝕤𝕞𝕚𝕥𝕥𝕖𝕕 𝕥𝕠 𝕒 𝕡𝕣𝕠𝕔𝕖𝕤𝕤𝕚𝕟𝕘 𝕦𝕟𝕚𝕥 𝕠𝕣 𝕔𝕠𝕟𝕥𝕣𝕠𝕝𝕝𝕖𝕣 𝕗𝕠𝕣 𝕚𝕟𝕥𝕖𝕣𝕡𝕣𝕖𝕥𝕒𝕥𝕚𝕠𝕟.
𝕋𝕪𝕡𝕖𝕤 𝕠𝕗 𝕊𝕖𝕟𝕤𝕠𝕣𝕤
𝕋𝕖𝕞𝕡𝕖𝕣𝕒𝕥𝕦𝕣𝕖 𝕊𝕖𝕟𝕤𝕠𝕣𝕤: 𝕄𝕖𝕒𝕤𝕦𝕣𝕖 𝕙𝕖𝕒𝕥 𝕠𝕣 𝕔𝕠𝕝𝕕, 𝕖.𝕘., 𝕥𝕙𝕖𝕣𝕞𝕠𝕔𝕠𝕦𝕡𝕝𝕖𝕤, ℝ𝕋𝔻𝕤.
ℙ𝕣𝕖𝕤𝕤𝕦𝕣𝕖 𝕊𝕖𝕟𝕤𝕠𝕣𝕤: 𝔻𝕖𝕥𝕖𝕔𝕥 𝕗𝕠𝕣𝕔𝕖 𝕡𝕖𝕣 𝕦𝕟𝕚𝕥 𝕒𝕣𝕖𝕒, 𝕖.𝕘., 𝕡𝕚𝕖𝕫𝕠𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔 𝕤𝕖𝕟𝕤𝕠𝕣𝕤.
ℙ𝕣𝕠𝕩𝕚𝕞𝕚𝕥𝕪 𝕊𝕖𝕟𝕤𝕠𝕣𝕤: 𝕊𝕖𝕟𝕤𝕖 𝕥𝕙𝕖 𝕡𝕣𝕖𝕤𝕖𝕟𝕔𝕖 𝕠𝕗 𝕟𝕖𝕒𝕣𝕓𝕪 𝕠𝕓𝕛𝕖𝕔𝕥𝕤 𝕨𝕚𝕥𝕙𝕠𝕦𝕥 𝕡𝕙𝕪𝕤𝕚𝕔𝕒𝕝 𝕔𝕠𝕟𝕥𝕒𝕔𝕥, 𝕖.𝕘., 𝕚𝕟𝕗𝕣𝕒𝕣𝕖𝕕 𝕠𝕣 𝕦𝕝𝕥𝕣𝕒𝕤𝕠𝕟𝕚𝕔 𝕤𝕖𝕟𝕤𝕠𝕣𝕤.
𝕃𝕚𝕘𝕙𝕥 𝕊𝕖𝕟𝕤𝕠𝕣𝕤: 𝔻𝕖𝕥𝕖𝕔𝕥 𝕝𝕚𝕘𝕙𝕥 𝕚𝕟𝕥𝕖𝕟𝕤𝕚𝕥𝕪, 𝕖.𝕘., 𝕡𝕙𝕠𝕥𝕠𝕕𝕚𝕠𝕕𝕖𝕤 𝕠𝕣 𝕃𝔻ℝ𝕤.
𝔸𝕡𝕡𝕝𝕚𝕔𝕒𝕥𝕚𝕠𝕟𝕤 𝕠𝕗 𝕊𝕖𝕟𝕤𝕠𝕣𝕤
𝔸𝕦𝕥𝕠𝕞𝕠𝕥𝕚𝕧𝕖 𝕚𝕟𝕕𝕦𝕤𝕥𝕣𝕪 (𝕖.𝕘., 𝕡𝕒𝕣𝕜𝕚𝕟𝕘 𝕒𝕤𝕤𝕚𝕤𝕥𝕒𝕟𝕔𝕖 𝕤𝕪𝕤𝕥𝕖𝕞𝕤).
𝕊𝕞𝕒𝕣𝕥 𝕙𝕠𝕞𝕖𝕤 (𝕖.𝕘., 𝕞𝕠𝕥𝕚𝕠𝕟 𝕕𝕖𝕥𝕖𝕔𝕥𝕠𝕣𝕤 𝕗𝕠𝕣 𝕤𝕖𝕔𝕦𝕣𝕚𝕥𝕪).
𝕀𝕟𝕕𝕦𝕤𝕥𝕣𝕚𝕒𝕝 𝕒𝕦𝕥𝕠𝕞𝕒𝕥𝕚𝕠𝕟 (𝕖.𝕘., 𝕞𝕠𝕟𝕚𝕥𝕠𝕣𝕚𝕟𝕘 𝕞𝕒𝕔𝕙𝕚𝕟𝕖𝕣𝕪
𝕎𝕙𝕒𝕥 𝔸𝕣𝕖 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤?

𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤 𝕒𝕣𝕖 𝕕𝕖𝕧𝕚𝕔𝕖𝕤 𝕣𝕖𝕤𝕡𝕠𝕟𝕤𝕚𝕓𝕝𝕖 𝕗𝕠𝕣 𝕥𝕒𝕜𝕚𝕟𝕘 𝕒𝕔𝕥𝕚𝕠𝕟 𝕓𝕒𝕤𝕖𝕕 𝕠𝕟 𝕤𝕚𝕘𝕟𝕒𝕝𝕤 𝕣𝕖𝕔𝕖𝕚𝕧𝕖𝕕 𝕗𝕣𝕠𝕞 𝕒 𝕔𝕠𝕟𝕥𝕣𝕠𝕝 𝕤𝕪𝕤𝕥𝕖𝕞. 𝕋𝕙𝕖𝕪 𝕔𝕠𝕟𝕧𝕖𝕣𝕥 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝 𝕖𝕟𝕖𝕣𝕘𝕪 𝕚𝕟𝕥𝕠 𝕞𝕖𝕔𝕙𝕒𝕟𝕚𝕔𝕒𝕝 𝕞𝕠𝕥𝕚𝕠𝕟 𝕥𝕠 𝕡𝕖𝕣𝕗𝕠𝕣𝕞 𝕒 𝕡𝕙𝕪𝕤𝕚𝕔𝕒𝕝 𝕥𝕒𝕤𝕜.

𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤 𝕒𝕣𝕖 𝕔𝕠𝕟𝕟𝕖𝕔𝕥𝕖𝕕 𝕒𝕥 𝕥𝕙𝕖 𝕠𝕦𝕥𝕡𝕦𝕥 𝕠𝕗 𝕒 𝕤𝕪𝕤𝕥𝕖𝕞. 𝕀𝕥 𝕥𝕒𝕜𝕖𝕤 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝 𝕤𝕚𝕘𝕟𝕒𝕝 𝕒𝕤 𝕚𝕥𝕤 𝕚𝕟𝕡𝕦𝕥 𝕒𝕟𝕕 𝕘𝕖𝕟𝕖𝕣𝕒𝕥𝕖𝕤 𝕞𝕖𝕔𝕙𝕒𝕟𝕚𝕔𝕒𝕝 𝕞𝕠𝕧𝕖𝕞𝕖𝕟𝕥 𝕒𝕤 𝕚𝕥𝕤 𝕠𝕦𝕥𝕡𝕦𝕥. 𝕀𝕥 𝕥𝕒𝕜𝕖𝕤 𝕥𝕙𝕖 𝕚𝕟𝕡𝕦𝕥 𝕗𝕣𝕠𝕞 𝕒 𝕤𝕪𝕤𝕥𝕖𝕞 𝕠𝕣 𝕒 𝕤𝕚𝕘𝕟𝕒𝕝 𝕔𝕠𝕟𝕕𝕚𝕥𝕚𝕠𝕟𝕚𝕟𝕘 𝕦𝕟𝕚𝕥 (𝕔𝕠𝕟𝕟𝕖𝕔𝕥𝕖𝕕 𝕨𝕚𝕥𝕙 𝕒 𝕤𝕖𝕟𝕤𝕠𝕣) 𝕒𝕟𝕕 𝕡𝕣𝕠𝕧𝕚𝕕𝕖𝕤 𝕠𝕦𝕥𝕡𝕦𝕥 𝕥𝕠 𝕥𝕙𝕖 𝕖𝕟𝕧𝕚𝕣𝕠𝕟𝕞𝕖𝕟𝕥.

𝕋𝕙𝕖 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣 𝕕𝕖𝕡𝕖𝕟𝕕𝕤 𝕠𝕟 𝕥𝕙𝕖 𝕕𝕒𝕥𝕒 𝕡𝕣𝕠𝕧𝕚𝕕𝕖𝕕 𝕓𝕪 𝕥𝕙𝕖 𝕤𝕖𝕟𝕤𝕠𝕣. 𝕋𝕙𝕖 𝕤𝕖𝕟𝕤𝕠𝕣 𝕡𝕣𝕠𝕧𝕚𝕕𝕖𝕤 𝕥𝕙𝕖 𝕕𝕒𝕥𝕒 𝕥𝕠 𝕒 𝕤𝕚𝕘𝕟𝕒𝕝 𝕔𝕠𝕟𝕕𝕚𝕥𝕚𝕠𝕟 𝕦𝕟𝕚𝕥 𝕠𝕣 𝕒 𝕤𝕪𝕤𝕥𝕖𝕞 𝕥𝕙𝕒𝕥 𝕡𝕣𝕠𝕔𝕖𝕤𝕤𝕖𝕤 𝕥𝕙𝕖 𝕕𝕒𝕥𝕒 𝕒𝕟𝕕 𝕓𝕒𝕤𝕖𝕕 𝕠𝕟 𝕥𝕙𝕒𝕥 𝕕𝕒𝕥𝕒 𝕚𝕥 𝕤𝕖𝕟𝕕𝕤 𝕔𝕠𝕞𝕞𝕒𝕟𝕕 𝕥𝕠 𝕥𝕙𝕖 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣. 𝔸𝕟 𝕖𝕩𝕒𝕞𝕡𝕝𝕖 𝕠𝕗 𝕤𝕦𝕔𝕙 𝕤𝕪𝕤𝕥𝕖𝕞 𝕚𝕤 𝕒 “𝕥𝕖𝕞𝕡𝕖𝕣𝕒𝕥𝕦𝕣𝕖 𝕔𝕠𝕟𝕥𝕣𝕠𝕝 𝕤𝕪𝕤𝕥𝕖𝕞”, 𝕨𝕙𝕖𝕣𝕖 𝕒 𝕥𝕖𝕞𝕡𝕖𝕣𝕒𝕥𝕦𝕣𝕖 𝕤𝕖𝕟𝕤𝕠𝕣 𝕞𝕠𝕟𝕚𝕥𝕠𝕣𝕤 𝕥𝕙𝕖 𝕥𝕖𝕞𝕡𝕖𝕣𝕒𝕥𝕦𝕣𝕖. 𝕀𝕗 𝕥𝕙𝕖 𝕥𝕖𝕞𝕡𝕖𝕣𝕒𝕥𝕦𝕣𝕖 𝕖𝕩𝕔𝕖𝕖𝕕𝕤 𝕒 𝕔𝕖𝕣𝕥𝕒𝕚𝕟 𝕝𝕚𝕞𝕚𝕥, 𝕥𝕙𝕖 𝕤𝕪𝕤𝕥𝕖𝕞 𝕤𝕖𝕟𝕕𝕤 𝕔𝕠𝕞𝕞𝕒𝕟𝕕 𝕥𝕠 𝕗𝕒𝕟 (𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣) 𝕥𝕠 𝕚𝕟𝕔𝕣𝕖𝕒𝕤𝕖 𝕚𝕥𝕤 𝕤𝕡𝕖𝕖𝕕 𝕒𝕟𝕕 𝕣𝕖𝕕𝕦𝕔𝕖 𝕥𝕙𝕖 𝕥𝕖𝕞𝕡𝕖𝕣𝕒𝕥𝕦𝕣𝕖. 𝔸𝕟𝕠𝕥𝕙𝕖𝕣 𝕖𝕩𝕒𝕞𝕡𝕝𝕖 𝕚𝕤 𝕒𝕦𝕥𝕠𝕞𝕒𝕥𝕚𝕔 𝕕𝕠𝕠𝕣 𝕥𝕙𝕒𝕥 𝕠𝕡𝕖𝕟𝕤 𝕨𝕙𝕖𝕟 𝕚𝕥 𝕤𝕖𝕟𝕤𝕖𝕤 𝕒 𝕡𝕖𝕣𝕤𝕠𝕟.

ℍ𝕠𝕨 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤 𝕎𝕠𝕣𝕜
𝕋𝕙𝕖 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣 𝕣𝕖𝕔𝕖𝕚𝕧𝕖𝕤 𝕒𝕟 𝕚𝕟𝕡𝕦𝕥 𝕤𝕚𝕘𝕟𝕒𝕝 𝕗𝕣𝕠𝕞 𝕒 𝕔𝕠𝕟𝕥𝕣𝕠𝕝𝕝𝕖𝕣.
𝕀𝕥 𝕥𝕣𝕒𝕟𝕤𝕝𝕒𝕥𝕖𝕤 𝕥𝕙𝕖 𝕤𝕚𝕘𝕟𝕒𝕝 𝕚𝕟𝕥𝕠 𝕞𝕖𝕔𝕙𝕒𝕟𝕚𝕔𝕒𝕝 𝕞𝕠𝕧𝕖𝕞𝕖𝕟𝕥 𝕠𝕣 𝕗𝕠𝕣𝕔𝕖.
𝕋𝕙𝕖 𝕞𝕠𝕧𝕖𝕞𝕖𝕟𝕥 𝕒𝕔𝕥𝕚𝕧𝕒𝕥𝕖𝕤 𝕠𝕣 𝕞𝕒𝕟𝕚𝕡𝕦𝕝𝕒𝕥𝕖𝕤 𝕒 𝕡𝕙𝕪𝕤𝕚𝕔𝕒𝕝 𝕡𝕣𝕠𝕔𝕖𝕤𝕤 𝕠𝕣 𝕞𝕖𝕔𝕙𝕒𝕟𝕚𝕤𝕞.
𝕋𝕪𝕡𝕖𝕤 𝕠𝕗 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤
𝕄𝕒𝕟𝕦𝕒𝕝 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣: 𝕊𝕦𝕔𝕙 𝕥𝕪𝕡𝕖 𝕠𝕗 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣 𝕚𝕤 𝕞𝕒𝕟𝕦𝕒𝕝𝕝𝕪 𝕔𝕠𝕟𝕥𝕣𝕠𝕝𝕝𝕖𝕕 𝕦𝕤𝕚𝕟𝕘 𝕘𝕖𝕒𝕣𝕤, 𝕝𝕖𝕧𝕖𝕣𝕤 𝕒𝕟𝕕 𝕨𝕙𝕖𝕖𝕝𝕤, 𝕖𝕥𝕔. 𝕋𝕙𝕖𝕪 𝕕𝕠 𝕟𝕠𝕥 𝕣𝕖𝕢𝕦𝕚𝕣𝕖 𝕒 𝕡𝕠𝕨𝕖𝕣 𝕤𝕠𝕦𝕣𝕔𝕖 𝕒𝕤 𝕥𝕙𝕖𝕪 𝕣𝕖𝕢𝕦𝕚𝕣𝕖 𝕙𝕦𝕞𝕒𝕟 𝕒𝕔𝕥𝕚𝕠𝕟.

𝔼𝕝𝕖𝕔𝕥𝕣𝕚𝕔 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣: 𝕊𝕦𝕔𝕙 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤 𝕣𝕖𝕢𝕦𝕚𝕣𝕖 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕚𝕥𝕪 𝕥𝕠 𝕠𝕡𝕖𝕣𝕒𝕥𝕖. 𝕀𝕥 𝕦𝕤𝕖𝕤 𝕒𝕟 𝕖𝕝𝕖𝕔𝕥𝕣𝕚𝕔𝕒𝕝 𝕞𝕠𝕥𝕠𝕣 𝕥𝕠 𝕘𝕖𝕟𝕖𝕣𝕒𝕥𝕖 𝕞𝕠𝕧𝕖𝕞𝕖𝕟𝕥. 𝕋𝕙𝕖𝕪 𝕒𝕣𝕖 𝕗𝕒𝕤𝕥 𝕒𝕟𝕕 𝕖𝕗𝕗𝕚𝕔𝕚𝕖𝕟𝕥.

ℍ𝕪𝕕𝕣𝕒𝕦𝕝𝕚𝕔 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣: ℍ𝕪𝕕𝕣𝕒𝕦𝕝𝕚𝕔 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤 𝕦𝕤𝕖 𝕔𝕠𝕞𝕡𝕣𝕖𝕤𝕤𝕖𝕕 𝕗𝕝𝕦𝕚𝕕 𝕚𝕟 𝕒 𝕔𝕪𝕝𝕚𝕟𝕕𝕖𝕣 𝕥𝕠 𝕘𝕖𝕟𝕖𝕣𝕒𝕥𝕖 𝕡𝕣𝕖𝕤𝕤𝕦𝕣𝕖 𝕥𝕙𝕒𝕥 𝕗𝕒𝕔𝕚𝕝𝕚𝕥𝕒𝕥𝕖𝕤 𝕞𝕖𝕔𝕙𝕒𝕟𝕚𝕔𝕒𝕝 𝕞𝕠𝕧𝕖𝕞𝕖𝕟𝕥.

ℙ𝕟𝕖𝕦𝕞𝕒𝕥𝕚𝕔 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣: ℙ𝕟𝕖𝕦𝕞𝕒𝕥𝕚𝕔 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤 𝕦𝕤𝕖 𝕘𝕒𝕤 𝕡𝕣𝕖𝕤𝕤𝕦𝕣𝕖 𝕥𝕠 𝕘𝕖𝕟𝕖𝕣𝕒𝕥𝕖 𝕞𝕠𝕧𝕖𝕞𝕖𝕟𝕥.

𝕊𝕡𝕣𝕚𝕟𝕘 𝔸𝕔𝕥𝕦𝕒𝕥𝕠𝕣: 𝕊𝕦𝕔𝕙 𝕒𝕔𝕥𝕦𝕒𝕥𝕠𝕣𝕤 𝕙𝕒𝕧𝕖 𝕒 𝕝𝕠𝕒𝕕𝕖𝕕 𝕤𝕡𝕣𝕚𝕟𝕘 𝕥𝕙𝕒𝕥 𝕚𝕤 𝕥𝕣𝕚𝕘𝕘𝕖𝕣𝕖𝕕 𝕒𝕟𝕕 𝕣𝕖𝕝𝕖𝕒𝕤𝕖𝕕 𝕥𝕠 𝕘𝕖𝕟𝕖𝕣𝕒𝕥𝕖 𝕞𝕖𝕔𝕙𝕒𝕟𝕚𝕔𝕒𝕝 𝕨𝕠𝕣𝕜. 𝕀𝕥 𝕔𝕒𝕟 𝕓𝕖 𝕥𝕣𝕚𝕘𝕘𝕖𝕣𝕖𝕕 𝕦𝕤𝕚𝕟𝕘 𝕤𝕖𝕧𝕖𝕣𝕒𝕝 𝕞𝕖𝕥𝕙𝕠𝕕𝕤.

24/12/2024

(𝚒)𝙡𝙖𝙧𝙜𝙚 𝙠𝙫𝙖 𝙧𝙖𝙩𝙞𝙣𝙜 𝙚𝙦𝙪𝙞𝙥𝙢𝙩 𝚃𝚑𝚎 𝚎𝚕𝚎𝚌𝚝𝚛𝚒𝚌𝚊𝚕 𝚖𝚊𝚌𝚑𝚒𝚗𝚎𝚛𝚢 (𝚎.𝚐., 𝚊𝚕𝚝𝚎𝚛𝚗𝚊𝚝𝚘𝚛𝚜, 𝚝𝚛𝚊𝚗𝚜𝚏𝚘𝚛𝚖𝚎𝚛𝚜,
𝚜𝚠𝚒𝚝𝚌𝚑𝚐𝚎𝚊𝚛) 𝚒𝚜 𝚊𝚕𝚠𝚊𝚢𝚜 𝚛𝚊𝚝𝚎𝚍 𝚒𝚗 *𝚔𝚅𝙰.
𝙽𝚘𝚠, 𝚔𝚅𝙰 = 𝚔𝚆
𝚌𝚘𝚜 φ
𝙸𝚝 𝚒𝚜 𝚌𝚕𝚎𝚊𝚛 𝚝𝚑𝚊𝚝 𝚔𝚅𝙰 𝚛𝚊𝚝𝚒𝚗𝚐 𝚘𝚏 𝚝𝚑𝚎 𝚎𝚚𝚞𝚒𝚙𝚖𝚎𝚗𝚝 𝚒𝚜 𝚒𝚗𝚟𝚎𝚛𝚜𝚎𝚕𝚢 𝚙𝚛𝚘𝚙𝚘𝚛𝚝𝚒𝚘𝚗𝚊𝚕 𝚝𝚘 𝚙𝚘𝚠𝚎𝚛 𝚏𝚊𝚌𝚝𝚘𝚛. 𝚃𝚑𝚎 𝚜𝚖𝚊𝚕𝚕𝚎𝚛
𝚝𝚑𝚎 𝚙𝚘𝚠𝚎𝚛 𝚏𝚊𝚌𝚝𝚘𝚛, 𝚝𝚑𝚎 𝚕𝚊𝚛𝚐𝚎𝚛 𝚒𝚜 𝚝𝚑𝚎 𝚔𝚅𝙰 𝚛𝚊𝚝𝚒𝚗𝚐. 𝚃𝚑𝚎𝚛𝚎𝚏𝚘𝚛𝚎, 𝚊𝚝 𝚕𝚘𝚠 𝚙𝚘𝚠𝚎𝚛 𝚏𝚊𝚌𝚝𝚘𝚛, 𝚝𝚑𝚎 𝚔𝚅𝙰 𝚛𝚊𝚝𝚒𝚗𝚐 𝚘𝚏 𝚝𝚑𝚎
𝚎𝚚𝚞𝚒𝚙𝚖𝚎𝚗𝚝 𝚑𝚊𝚜 𝚝𝚘 𝚋𝚎 𝚖𝚊𝚍𝚎 𝚖𝚘𝚛𝚎, 𝚖𝚊𝚔𝚒𝚗𝚐 𝚝𝚑𝚎 𝚎𝚚𝚞𝚒𝚙𝚖𝚎𝚗𝚝 𝚕𝚊𝚛𝚐𝚎𝚛 𝚊𝚗𝚍 𝚎𝚡𝚙𝚎𝚗𝚜𝚒𝚟𝚎.
(𝚒𝚒) 𝙜𝙧𝙚𝙖𝙩𝙚𝙧 𝙘𝙤𝙣𝙙𝙪𝙘𝙩𝙤𝙧 𝙨𝙞𝙯𝙚 . 𝚃𝚘 𝚝𝚛𝚊𝚗𝚜𝚖𝚒𝚝 𝚘𝚛 𝚍𝚒𝚜𝚝𝚛𝚒𝚋𝚞𝚝𝚎 𝚊 𝚏𝚒𝚡𝚎𝚍 𝚊𝚖𝚘𝚞𝚗𝚝 𝚘𝚏 𝚙𝚘𝚠𝚎𝚛 𝚊𝚝 𝚌𝚘𝚗𝚜𝚝𝚊𝚗𝚝
𝚟𝚘𝚕𝚝𝚊𝚐𝚎, 𝚝𝚑𝚎 𝚌𝚘𝚗𝚍𝚞𝚌𝚝𝚘𝚛 𝚠𝚒𝚕𝚕 𝚑𝚊𝚟𝚎 𝚝𝚘 𝚌𝚊𝚛𝚛𝚢 𝚖𝚘𝚛𝚎 𝚌𝚞𝚛𝚛𝚎𝚗𝚝 𝚊𝚝 𝚕𝚘𝚠 𝚙𝚘𝚠𝚎𝚛 𝚏𝚊𝚌𝚝𝚘𝚛.
Large copper losses. The large current at low power factor causes more
losses in all the
elements of the supply system. This results in poor efficiency.
(iv) Poor voltage regulation. The large current at low lagging power factor causes greater
voltage drops in alternators, transformers, transmission lines and distributors. This results
in the decreased voltage available at the supply end, thus impairing the performance of
utilisation devices. In order to keep the receiving end voltage within permissible limits,
extra equipment (i.e., voltage regulators) is required.
(v) Reduced handling capacity of system. The lagging power factor reduces the handling
capacity of all the elements of the system. It is because the reactive component of current
prevents the full utilisation of installed capacity.

23/12/2024

𝘾𝙖𝙪𝙨𝙚𝙨 𝙤𝙛 𝙥𝙤𝙬𝙚𝙧 𝙛𝙖𝙘𝙩𝙤𝙧
Low power factor is undesirable from economic point of view. Normally, the power factor of the
whole load on the supply system in lower than 0·8. The following are the causes of low power factor:
(i) Most of the a.c. motors are of induction type (1φ and 3φ induction motors) which have low
lagging power factor. These motors work at a power factor which is extremely small on
light load (0·2 to 0·3) and rises to 0·8 or 0·9 at full load.
(ii) Arc lamps, electric discharge lamps and industrial heating furnaces operate at low lagging
power factor.
(iii) The load on the power system is varying ; being high during morning and evening and low at
other times. During low load period, supply voltage is increased which increases the
magnetisation current. This results in the decreased power factor.

22/12/2024

𝙿𝚘𝚠𝚎𝚛 𝚏𝚊𝚌𝚝𝚘𝚛 𝚒𝚖𝚙𝚛𝚘𝚟𝚎𝚖𝚎𝚗𝚝 𝚎𝚚𝚞𝚒𝚙𝚖𝚎𝚗𝚝 3
𝙎𝙩𝙖𝙩𝙞𝙘 𝙘𝙖𝙥𝙖𝙘𝙞𝙩𝙤𝙧. The power factor can be improved by connecting capacitors in parallel
with the equipment operating at lagging power factor. The capacitor (generally known as staticcapacitor) draws a leading current and partly or completely neutralises the lagging reactive compo-
nent of load current. This raises the power factor of the load. For three-phase loads, the capacitors
can be connected in delta or star . Static capacitors are invariably used for power
factor improvement in factories.

21/12/2024

Power factor improvement equipment 2
ℙ𝕙𝕒𝕤𝕖 𝕒𝕕𝕧𝕒𝕟𝕔𝕖𝕣. Phase advancers are used to
improve the power factor of induction motors. The low
power factor of an induction motor is due to the fact that
its stator winding draws exciting current which lags be-
hind the supply voltage by 90o If the exciting ampere
turns can be provided from some other a.c. source, then
the stator winding will be relieved of exciting current and
the power factor of the motor can be improved. This job
is accomplished by the phase advancer which is simply an a.c. exciter. The phase advancer is mounted
on the same shaft as the main motor and is connected in the rotor circuit of the motor. It provides
exciting ampere turns to the rotor circuit at slip frequency. By providing more ampere turns than
required, the induction motor can be made to operate on leading power factor like an over-excited
synchronous motor.
Phase advancers have two principal advantages. Firstly, as the exciting ampere turns are sup-
plied at slip frequency, therefore, lagging kVAR drawn by the motor are considerably reduced. Sec-
ondly, phase advancer can be conveniently used where the use of synchronous motors is unadmissible.
However, the major disadvantage of phase advancers is that they are not economical for motors
below 200 H.P.

20/12/2024

Power Factor Improvement equipment
Synchronous condenser. A synchronous motor takes a leading current when over-excited
and, therefore, behaves as a capacitor. An over-excited synchronous motor running on no load is
known as synchronous condenser. When such a machine is connected in parallel with the supply, it
takes a leading current which partly neutralises the lagging reactive component of the load. Thus the
power factor is improved.
Fig 6.5 shows the power factor improvement by synchronous condenser method. The 3φ load takes
current IL at low lagging power factor cos φL. The synchronous condenser takes a current Im which
leads the voltage by an angle φm*. The resultant current I is the phasor sum of Im and IL and lags
behind the voltage by an angle φ. It is clear that φ is less than φL so that cos φ is greater than cos φL.
Thus the power factor is increased from cos φL to cos φ. Synchronous condensers are generally used
at major bulk supply substations for power factor improvement.

19/12/2024

Electrical power generation and transmission

18/12/2024