4. 𝘚𝘰𝘭𝘥𝘦𝘳𝘪𝘯𝘨 𝘐𝘳𝘰𝘯
𝘋𝘰 𝘤𝘰𝘮𝘱𝘰𝘯𝘦𝘯𝘵𝘴 𝘬𝘰 𝘩𝘢𝘮𝘦𝘴𝘩𝘢 𝘬𝘦 𝘭𝘪𝘺𝘦 𝘫𝘰𝘥𝘯𝘦 𝘬𝘦 𝘭𝘪𝘺𝘦 𝘪𝘴𝘬𝘢 𝘶𝘴𝘦 𝘩𝘰𝘵𝘢 𝘩𝘢𝘪.

𝘗𝘊𝘉 𝘙𝘦𝘱𝘢𝘪𝘳: 𝘒𝘪𝘴𝘪 𝘱𝘶𝘳𝘢𝘯𝘦 𝘦𝘭𝘦𝘤𝘵𝘳𝘰𝘯𝘪𝘤 𝘣𝘰𝘢𝘳𝘥 𝘬𝘰 𝘵𝘩𝘦𝘦𝘬 𝘬𝘢𝘳𝘯𝘦 𝘺𝘢 𝘯𝘢𝘺𝘢 𝘣𝘢𝘯𝘢𝘯𝘦 𝘬𝘦 𝘭𝘪𝘺𝘦.

𝘑𝘰𝘪𝘯𝘵𝘴: 𝘔𝘢𝘻𝘣𝘰𝘰𝘵 𝘦𝘭𝘦𝘤𝘵𝘳𝘪𝘤𝘢𝘭 𝘤𝘰𝘯𝘯𝘦𝘤𝘵𝘪𝘰𝘯 𝘣𝘢𝘯𝘢𝘯𝘦 𝘬𝘦 𝘭𝘪𝘺𝘦 𝘴𝘰𝘭𝘥𝘦𝘳𝘪𝘯𝘨 𝘸𝘪𝘳𝘦 𝘬𝘰 𝘱𝘪𝘨𝘩𝘭𝘢 𝘬𝘢𝘳 𝘭𝘢𝘨𝘢𝘺𝘢 𝘫𝘢𝘵𝘢 𝘩𝘢𝘪.

5. 𝘗𝘰𝘸𝘦𝘳 𝘚𝘶𝘱𝘱𝘭𝘺
𝘠𝘦𝘩 𝘬𝘪𝘴𝘪 𝘣𝘩𝘪 𝘤𝘪𝘳𝘤𝘶𝘪𝘵 𝘬𝘰 𝘤𝘩𝘢𝘭𝘢𝘯𝘦 𝘬𝘦 𝘭𝘪𝘺𝘦 𝘣𝘪𝘫𝘭𝘪 𝘬𝘢 𝘴𝘰𝘶𝘳𝘤𝘦 𝘩𝘰𝘵𝘢 𝘩𝘢𝘪.

𝘛𝘦𝘴𝘵𝘪𝘯𝘨: 𝘑𝘢𝘣 𝘢𝘢𝘱 𝘬𝘰𝘪 𝘯𝘢𝘺𝘢 𝘱𝘳𝘰𝘫𝘦𝘤𝘵 𝘣𝘢𝘯𝘢𝘵𝘦 𝘩𝘢𝘪𝘯, 𝘵𝘰𝘩 𝘶𝘴𝘦 𝘢𝘭𝘢𝘨-𝘢𝘭𝘢𝘨 𝘷𝘰𝘭𝘵𝘢𝘨𝘦 (𝘫𝘢𝘪𝘴𝘦 5𝘝, 12𝘝) 𝘥𝘦𝘬𝘢𝘳 𝘵𝘦𝘴𝘵 𝘬𝘢𝘳𝘯𝘦 𝘬𝘦 𝘭𝘪𝘺𝘦 𝘪𝘴𝘬𝘢 𝘶𝘴𝘦 𝘩𝘰𝘵𝘢 𝘩𝘢𝘪.

𝘚𝘢𝘧𝘦𝘵𝘺: 𝘐𝘴𝘴𝘦 𝘩𝘶𝘮 𝘤𝘶𝘳𝘳𝘦𝘯𝘵 𝘭𝘪𝘮𝘪𝘵 𝘴𝘦𝘵 𝘬𝘢𝘳 𝘴𝘢𝘬𝘵𝘦 𝘩𝘢𝘪𝘯 𝘵𝘢𝘢𝘬𝘪 𝘩𝘢𝘮𝘢𝘳𝘢 𝘤𝘪𝘳𝘤𝘶𝘪𝘵 𝘫𝘢𝘭𝘯𝘦 𝘴𝘦 𝘣𝘢𝘤𝘩 𝘫𝘢𝘺𝘦

6. 𝘗𝘭𝘪𝘦𝘳𝘴, 𝘊𝘶𝘵𝘵𝘦𝘳𝘴 𝘢𝘶𝘳 𝘚𝘤𝘳𝘦𝘸𝘥𝘳𝘪𝘷𝘦𝘳𝘴
𝘠𝘦𝘩 𝘣𝘢𝘴𝘪𝘤 𝘮𝘢𝘯𝘶𝘢𝘭 𝘵𝘰𝘰𝘭𝘴 𝘩𝘢𝘪𝘯 𝘫𝘰 𝘩𝘢𝘳 𝘬𝘢𝘢𝘮 𝘮𝘦𝘪𝘯 𝘢𝘢𝘵𝘦 𝘩𝘢𝘪𝘯.

𝘚𝘪𝘥𝘦 𝘊𝘶𝘵𝘵𝘦𝘳: 𝘌𝘹𝘵𝘳𝘢 𝘸𝘪𝘳𝘦𝘴 𝘬𝘰 𝘬𝘢𝘢𝘵𝘯𝘦 𝘬𝘦 𝘭𝘪𝘺𝘦.

𝘗𝘭𝘪𝘦𝘳𝘴: 𝘞𝘪𝘳𝘦𝘴 𝘬𝘰 𝘮𝘰𝘥𝘯𝘦 𝘺𝘢 𝘱𝘢𝘬𝘢𝘥𝘯𝘦 𝘬𝘦 𝘭𝘪𝘺𝘦.

𝘚𝘤𝘳𝘦𝘸𝘥𝘳𝘪𝘷𝘦𝘳: 𝘌𝘭𝘦𝘤𝘵𝘳𝘪𝘤𝘢𝘭 𝘱𝘢𝘯𝘦𝘭𝘴 𝘺𝘢 𝘨𝘢𝘥𝘨𝘦𝘵𝘴 𝘬𝘰 𝘬𝘩𝘰𝘭𝘯𝘦 𝘢𝘶𝘳 𝘣𝘢𝘯𝘥 𝘬𝘢𝘳𝘯𝘦 𝘬𝘦 𝘭𝘪𝘺𝘦.

ᴛᴏᴘɪᴄ: ᴍᴀꜱᴛᴇʀɪɴɢ ᴄɪʀᴄᴜɪᴛ ᴀɴᴀʟʏꜱɪꜱ: ᴋɪʀᴄʜʜᴏꜰꜰ’ꜱ ʟᴀᴡꜱ ⚡️

ɪꜰ ᴏʜᴍ’ꜱ ʟᴀᴡ ɪꜱ ᴛʜᴇ ꜰᴏᴜɴᴅᴀᴛɪᴏɴ, ᴋɪʀᴄʜʜᴏꜰꜰ’ꜱ ʟᴀᴡꜱ ᴀʀᴇ ᴛʜᴇ ʀᴜʟᴇꜱ ᴏꜰ ᴛʜᴇ ɢᴀᴍᴇ. ᴇᴠᴇʀʏ ᴄᴏᴍᴘʟᴇx ᴄɪʀᴄᴜɪᴛ ꜰᴏʟʟᴏᴡꜱ ᴛʜᴇꜱᴇ ᴛᴡᴏ ꜱɪᴍᴘʟᴇ ᴘʀɪɴᴄɪᴘʟᴇꜱ:
1️⃣ ᴋɪʀᴄʜʜᴏꜰꜰ’ꜱ ᴄᴜʀʀᴇɴᴛ ʟᴀᴡ (ᴋᴄʟ): ᴛʜᴇ "ᴊᴜɴᴄᴛɪᴏɴ ʀᴜʟᴇ." ᴛᴏᴛᴀʟ ᴄᴜʀʀᴇɴᴛ ᴇɴᴛᴇʀɪɴɢ ᴀ ᴊᴜɴᴄᴛɪᴏɴ ᴍᴜꜱᴛ ᴇQᴜᴀʟ ᴛʜᴇ ᴛᴏᴛᴀʟ ᴄᴜʀʀᴇɴᴛ ʟᴇᴀᴠɪɴɢ ɪᴛ. ᴄᴏɴᴄᴇᴘᴛ: ᴄʜᴀʀɢᴇ ᴄᴀɴɴᴏᴛ ʙᴇ ʟᴏꜱᴛ; ɪᴛ ᴊᴜꜱᴛ ꜰʟᴏᴡꜱ ᴛʜʀᴏᴜɢʜ! 🌊

2️⃣ ᴋɪʀᴄʜʜᴏꜰꜰ’ꜱ ᴠᴏʟᴛᴀɢᴇ ʟᴀᴡ (ᴋᴠʟ): ᴛʜᴇ "ʟᴏᴏᴘ ʀᴜʟᴇ." ᴛʜᴇ ꜱᴜᴍ ᴏꜰ ᴀʟʟ ᴇʟᴇᴄᴛʀɪᴄᴀʟ ᴘᴏᴛᴇɴᴛɪᴀʟ ᴅɪꜰꜰᴇʀᴇɴᴄᴇꜱ (ᴠᴏʟᴛᴀɢᴇ) ᴀʀᴏᴜɴᴅ ᴀɴʏ ᴄʟᴏꜱᴇᴅ ʟᴏᴏᴘ ɪꜱ ᴢᴇʀᴏ. ᴄᴏɴᴄᴇᴘᴛ: ᴇɴᴇʀɢʏ ɢᴀɪɴᴇᴅ ᴍᴜꜱᴛ ᴇQᴜᴀʟ ᴇɴᴇʀɢʏ ʟᴏꜱᴛ ɪɴ ᴀ ᴄɪʀᴄᴜɪᴛ. 🔄

ꜰᴏʀᴍᴜʟᴀᴇ ᴛᴏ ʀᴇᴍᴇᴍʙᴇʀ:ᴋᴄʟ: $\ꜱᴜᴍ ɪ_{ɪɴ} = \ꜱᴜᴍ ɪ_{ᴏᴜᴛ}$ᴋᴠʟ: $\ꜱᴜᴍ ᴠ = 0$ᴡʜɪᴄʜ ᴏɴᴇ ᴅᴏ ʏᴏᴜ ꜰɪɴᴅ ᴇᴀꜱɪᴇʀ ᴛᴏ ᴀᴘᴘʟʏ ɪɴ ᴄᴏᴍᴘʟᴇx ɴᴏᴅᴀʟ ᴀɴᴀʟʏꜱɪꜱ? ᴋᴄʟ ᴏʀ ᴋᴠʟ?

𝘖𝘷𝘦𝘳𝘭𝘰𝘢𝘥 𝘗𝘳𝘰𝘵𝘦𝘤𝘵𝘪𝘰𝘯 (𝘛𝘩𝘦𝘳𝘮𝘢𝘭 𝘖𝘷𝘦𝘳𝘭𝘰𝘢𝘥 𝘙𝘦𝘭𝘢𝘺)
𝘞𝘩𝘦𝘯 𝘢 𝘮𝘰𝘵𝘰𝘳 𝘤𝘢𝘳𝘳𝘪𝘦𝘴 𝘢 𝘭𝘰𝘢𝘥 𝘣𝘦𝘺𝘰𝘯𝘥 𝘪𝘵𝘴 𝘳𝘢𝘵𝘦𝘥 𝘤𝘢𝘱𝘢𝘤𝘪𝘵𝘺, 𝘵𝘩𝘦 𝘤𝘶𝘳𝘳𝘦𝘯𝘵 𝘧𝘭𝘰𝘸𝘪𝘯𝘨 𝘵𝘩𝘳𝘰𝘶𝘨𝘩 𝘵𝘩𝘦 𝘸𝘪𝘯𝘥𝘪𝘯𝘨𝘴 𝘪𝘯𝘤𝘳𝘦𝘢𝘴𝘦𝘴 𝘴𝘪𝘨𝘯𝘪𝘧𝘪𝘤𝘢𝘯𝘵𝘭𝘺. 𝘛𝘩𝘪𝘴 𝘦𝘹𝘤𝘦𝘴𝘴𝘪𝘷𝘦 𝘤𝘶𝘳𝘳𝘦𝘯𝘵 𝘭𝘦𝘢𝘥𝘴 𝘵𝘰 𝘵𝘩𝘦 𝘨𝘦𝘯𝘦𝘳𝘢𝘵𝘪𝘰𝘯 𝘰𝘧 𝘩𝘪𝘨𝘩 𝘩𝘦𝘢𝘵 (𝘐
2:
𝘙 𝘭𝘰𝘴𝘴𝘦𝘴), 𝘸𝘩𝘪𝘤𝘩 𝘤𝘢𝘯 𝘥𝘢𝘮𝘢𝘨𝘦 𝘵𝘩𝘦 𝘪𝘯𝘴𝘶𝘭𝘢𝘵𝘪𝘰𝘯 𝘢𝘯𝘥 𝘭𝘦𝘢𝘥 𝘵𝘰 𝘮𝘰𝘵𝘰𝘳 𝘧𝘢𝘪𝘭𝘶𝘳𝘦.

• 𝘏𝘰𝘸 𝘪𝘵 𝘸𝘰𝘳𝘬𝘴: 𝘛𝘩𝘪𝘴 𝘱𝘳𝘰𝘵𝘦𝘤𝘵𝘪𝘰𝘯 𝘴𝘤𝘩𝘦𝘮𝘦 𝘵𝘺𝘱𝘪𝘤𝘢𝘭𝘭𝘺 𝘶𝘵𝘪𝘭𝘪𝘻𝘦𝘴 𝘉𝘪𝘮𝘦𝘵𝘢𝘭𝘭𝘪𝘤 𝘖𝘷𝘦𝘳𝘭𝘰𝘢𝘥 𝘙𝘦𝘭𝘢𝘺𝘴.

• 𝘛𝘩𝘦 𝘔𝘦𝘤𝘩𝘢𝘯𝘪𝘴𝘮: 𝘛𝘩𝘦 𝘳𝘦𝘭𝘢𝘺 𝘤𝘰𝘯𝘵𝘢𝘪𝘯𝘴 𝘢 𝘣𝘪𝘮𝘦𝘵𝘢𝘭𝘭𝘪𝘤 𝘴𝘵𝘳𝘪𝘱 (𝘮𝘢𝘥𝘦 𝘰𝘧 𝘵𝘸𝘰 𝘮𝘦𝘵𝘢𝘭𝘴 𝘸𝘪𝘵𝘩 𝘥𝘪𝘧𝘧𝘦𝘳𝘦𝘯𝘵 𝘦𝘹𝘱𝘢𝘯𝘴𝘪𝘰𝘯 𝘳𝘢𝘵𝘦𝘴).