Question

14. Compare the power used in the 2 ohm resistor in each of the following circuits
(i) a 6 V battery in series with 1 ohm and 2 ohm resistors, and (ii) a 4 V battery in parallel
with 12ohm and 2ohm resistors.​

Answer 1

Answer:

(ɪ) ᴘᴏᴛᴇɴᴛɪᴀʟ ᴅɪғғᴇʀᴇɴᴄᴇ, ᴠ = 6 ᴠ

1ᴏʜᴍ ᴀɴᴅ 2 ᴏʜᴍ ʀᴇsɪsᴛᴏʀs ᴀʀᴇ ᴄᴏɴɴᴇᴄᴛᴇᴅ ɪɴ sᴇʀɪᴇs. ᴛʜᴇʀᴇғᴏʀᴇ, ᴇϙᴜɪᴠᴀʟᴇɴᴛ ʀᴇsɪsᴛᴀɴᴄᴇ ᴏғ ᴛʜᴇ ᴄɪʀᴄᴜɪᴛ, ʀ = 1 + 2 = 3 ᴏʜᴍ

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴏʜᴍ’s ʟᴀᴡ,

ᴠ = ɪʀ

ᴡʜᴇʀᴇ,

ɪ ɪs ᴛʜᴇ ᴄᴜʀʀᴇɴᴛ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ᴄɪʀᴄᴜɪᴛ

ɪ= 6/3 = 2 ᴀ

ᴛʜɪs ᴄᴜʀʀᴇɴᴛ ᴡɪʟʟ ғʟᴏᴡ ᴛʜʀᴏᴜɢʜ ᴇᴀᴄʜ ᴄᴏᴍᴘᴏɴᴇɴᴛ ᴏғ ᴛʜᴇ ᴄɪʀᴄᴜɪᴛ ʙᴇᴄᴀᴜsᴇ ᴛʜᴇʀᴇ ɪs ɴᴏ ᴅɪᴠɪsɪᴏɴ ᴏғ ᴄᴜʀʀᴇɴᴛ ɪɴ sᴇʀɪᴇs ᴄɪʀᴄᴜɪᴛs. ʜᴇɴᴄᴇ, ᴄᴜʀʀᴇɴᴛ ғʟᴏᴡɪɴɢ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ 2ᴏʜᴍ ʀᴇsɪsᴛᴏʀ ɪs 2 ᴀ. ᴘᴏᴡᴇʀ ɪs ɢɪᴠᴇɴ ʙʏ ᴛʜᴇ ᴇxᴘʀᴇssɪᴏɴ,

ᴘ= (ɪ)2ʀ = (2)2 x 2 = 8 ᴡ

(ɪɪ) ᴘᴏᴛᴇɴᴛɪᴀʟ ᴅɪғғᴇʀᴇɴᴄᴇ, ᴠ = 4 ᴠ

12 ᴏʜᴍ ᴀɴᴅ 2 ᴏʜᴍ ʀᴇsɪsᴛᴏʀs ᴀʀᴇ ᴄᴏɴɴᴇᴄᴛᴇᴅ ɪɴ ᴘᴀʀᴀʟʟᴇʟ. ᴛʜᴇ ᴠᴏʟᴛᴀɢᴇ ᴀᴄʀᴏss ᴇᴀᴄʜ ᴄᴏᴍᴘᴏɴᴇɴᴛ ᴏғ ᴀ ᴘᴀʀᴀʟʟᴇʟ ᴄɪʀᴄᴜɪᴛ ʀᴇᴍᴀɪɴs ᴛʜᴇ sᴀᴍᴇ. ʜᴇɴᴄᴇ, ᴛʜᴇ ᴠᴏʟᴛᴀɢᴇ ᴀᴄʀᴏss 2 ᴏʜᴍ ʀᴇsɪsᴛᴏʀ ᴡɪʟʟ ʙᴇ 4 ᴠ.

ᴘᴏᴡᴇʀ ᴄᴏɴsᴜᴍᴇᴅ ʙʏ 2 ᴏʜᴍ ʀᴇsɪsᴛᴏʀ ɪs ɢɪᴠᴇɴ ʙʏ

ᴘ= ᴠ2/ʀ = 42/2 = 8 ᴡ

ᴛʜᴇʀᴇғᴏʀᴇ, ᴛʜᴇ ᴘᴏᴡᴇʀ ᴜsᴇᴅ ʙʏ 2 ᴏʜᴍ ʀᴇsɪsᴛᴏʀ ɪs 8 ᴡ.

Explanation:

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