Question

Derive the current division formula for two branch parallel circuit?​

Answer 1

$\huge{\underline{\mathtt{\red{A}\pink{N} \green{S}\blue{W} \purple{E}\orange{R}}}}$

We can check our calculations as according to Kirchhoff's Current Rule, all the branch currents will be equal to the total current, so: IT = IR1 + IR2 + IR3 = 10 + 4 + 1 = 15 amperes, as expected. Thus we can see that the total current, IT is divided according to a simple ratio determined by the branch resistances....

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Answer 2

Explanation:

ᴡᴇ ᴄᴀɴ ᴄʜᴇᴄᴋ ᴏᴜʀ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ ᴀꜱ ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴋɪʀᴄʜʜᴏꜰꜰ'ꜱ ᴄᴜʀʀᴇɴᴛ ʀᴜʟᴇ, ᴀʟʟ ᴛʜᴇ ʙʀᴀɴᴄʜ ᴄᴜʀʀᴇɴᴛꜱ ᴡɪʟʟ ʙᴇ ᴇQᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴛᴏᴛᴀʟ ᴄᴜʀʀᴇɴᴛ, ꜱᴏ: ɪᴛ = ɪʀ1 + ɪʀ2 + ɪʀ3 = 10 + 4 + 1 = 15 ᴀᴍᴘᴇʀᴇꜱ, ᴀꜱ ᴇxᴘᴇᴄᴛᴇᴅ. ᴛʜᴜꜱ ᴡᴇ ᴄᴀɴ ꜱᴇᴇ ᴛʜᴀᴛ ᴛʜᴇ ᴛᴏᴛᴀʟ ᴄᴜʀʀᴇɴᴛ, ɪᴛ ɪꜱ ᴅɪᴠɪᴅᴇᴅ ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴀ ꜱɪᴍᴘʟᴇ ʀᴀᴛɪᴏ ᴅᴇᴛᴇʀᴍɪɴᴇᴅ ʙʏ ᴛʜᴇ ʙʀᴀɴᴄʜ ʀᴇꜱɪꜱᴛᴀɴᴄᴇꜱ

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