Question

What is the equivalent resistance of the network between points A and B? (each resistance is of value r)
A)r/2
B) 4r
C)r/4
D) Zero​

Answer 1

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$\huge\boxed{\fcolorbox{cyan}{pink}{❦ \: Qᴜᴇsᴛɪᴏɴ}}$

❍ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ᴇQᴜɪᴠᴀʟᴇɴᴛ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ᴏꜰ ᴛʜᴇ ɴᴇᴛᴡᴏʀᴋ ʙᴇᴛᴡᴇᴇɴ ᴘᴏɪɴᴛꜱ ᴀ ᴀɴᴅ ʙ? (ᴇᴀᴄʜ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ɪꜱ ᴏꜰ ᴠᴀʟᴜᴇ ʀ)

ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ᴇQᴜɪᴠᴀʟᴇɴᴛ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ᴏꜰ ᴛʜᴇ ɴᴇᴛᴡᴏʀᴋ ʙᴇᴛᴡᴇᴇɴ ᴘᴏɪɴᴛꜱ ᴀ ᴀɴᴅ ʙ? (ᴇᴀᴄʜ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ɪꜱ ᴏꜰ ᴠᴀʟᴜᴇ ʀ)ᴀ)ʀ/2

ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ᴇQᴜɪᴠᴀʟᴇɴᴛ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ᴏꜰ ᴛʜᴇ ɴᴇᴛᴡᴏʀᴋ ʙᴇᴛᴡᴇᴇɴ ᴘᴏɪɴᴛꜱ ᴀ ᴀɴᴅ ʙ? (ᴇᴀᴄʜ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ɪꜱ ᴏꜰ ᴠᴀʟᴜᴇ ʀ)ᴀ)ʀ/2ʙ) 4ʀ

ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ᴇQᴜɪᴠᴀʟᴇɴᴛ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ᴏꜰ ᴛʜᴇ ɴᴇᴛᴡᴏʀᴋ ʙᴇᴛᴡᴇᴇɴ ᴘᴏɪɴᴛꜱ ᴀ ᴀɴᴅ ʙ? (ᴇᴀᴄʜ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ɪꜱ ᴏꜰ ᴠᴀʟᴜᴇ ʀ)ᴀ)ʀ/2ʙ) 4ʀᴄ)ʀ/4

ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ᴇQᴜɪᴠᴀʟᴇɴᴛ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ᴏꜰ ᴛʜᴇ ɴᴇᴛᴡᴏʀᴋ ʙᴇᴛᴡᴇᴇɴ ᴘᴏɪɴᴛꜱ ᴀ ᴀɴᴅ ʙ? (ᴇᴀᴄʜ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ɪꜱ ᴏꜰ ᴠᴀʟᴜᴇ ʀ)ᴀ)ʀ/2ʙ) 4ʀᴄ)ʀ/4ᴅ) ᴢᴇʀᴏ

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$\huge\boxed{\fcolorbox{cyan}{pink}{❦ \: Aɴsᴡᴇʀ}}$

$\huge \mathtt{ ✰\frac{4}{r}}$

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$\huge\boxed{\fcolorbox{cyan}{pink}{❍ᴇxᴘʟᴀɴᴀᴛɪᴏɴ}}$

ᴀʟʟ ᴏꜰ ᴛʜᴇᴍ ʟɪᴇꜱ ɪɴ ᴘᴀʀᴇʟʟᴇʟ ᴀʀʀᴀɴɢᴇᴍᴇɴᴛ,

ᴀʟʟ ᴏꜰ ᴛʜᴇᴍ ʟɪᴇꜱ ɪɴ ᴘᴀʀᴇʟʟᴇʟ ᴀʀʀᴀɴɢᴇᴍᴇɴᴛ,ɪꜰ ᴡᴇ ᴇꜱᴄᴀᴘᴇ ᴏᴜᴛ ᴛʜᴇ ᴡɪʀᴇ ,ᴅᴏᴇꜱ ɴᴏᴛ ʜᴀᴠᴇ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ..

ᴀʟʟ ᴏꜰ ᴛʜᴇᴍ ʟɪᴇꜱ ɪɴ ᴘᴀʀᴇʟʟᴇʟ ᴀʀʀᴀɴɢᴇᴍᴇɴᴛ,ɪꜰ ᴡᴇ ᴇꜱᴄᴀᴘᴇ ᴏᴜᴛ ᴛʜᴇ ᴡɪʀᴇ ,ᴅᴏᴇꜱ ɴᴏᴛ ʜᴀᴠᴇ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ..ᴛʜᴇɴ ᴀʟʟ ᴛᴇʀᴍɪɴᴀʟ ᴏꜰ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ᴡɪʟʟ ꜰᴏʀᴍ ᴘᴀʀᴇʟʟᴇʟ ᴀʀʀᴀɴɢᴇᴍᴇɴᴛ....

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