Question

Two resistances when connected in parallel give resultant value of 2ohm, when connected in series give value of 9ohm. Calculate the value of each resistance.

Answer 1

Let two resistances be x & y.
1. Parellel = 2ohm
2. Series = 9ohm
1. x+y = 9
2. xy/x+y =2

Therefore, 9=xy/2,
& xy=18,
x=18/y,

Therefore, 18/y + y = 9,

y^2 - 3y - 6y + 18 = 0,
y(y-3) -6(y-3)=0,
Therefore, y=6 or y=3,
Hence, x=3 or x=6 respectively.

Answer 2

$\huge\mathfrak{Bonjour!!}$

$\huge\fcolorbox{black}{aqua}{Solution:-}$

✒ ᴀɴsᴡᴇʀ:-

⛄ ✴ ʀ1 = 6 Ω ᴀɴᴅ

✴ ʀ2 = 3 Ω

✒ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

⛄ ʟᴇᴛ ʀ1 ᴀɴᴅ ʀ2 ʙᴇ ᴛᴡᴏ ʀᴇsɪsᴛᴀɴᴄᴇs.

ᴡʜᴇɴ ᴄᴏɴɴᴇᴄᴛᴇᴅ ɪɴ sᴇʀɪᴇs,

★ ʀ1 + ʀ2 = 9 Ω

ᴡʜᴇɴ ᴄᴏɴɴᴇᴄᴛᴇᴅ ɪɴ ᴘᴀʀᴀʟʟᴇʟ,

★ 1/ʀ1 + 1/ʀ2 = 1/2

=> ʀ1 + ʀ2 /ʀ1ʀ2 = 1/2

=> 9/ʀ1ʀ2 = 1/2

=> ʀ1ʀ2 = 18

ɴᴏᴡ,

(ʀ1 - ʀ2)² = (ʀ1 + ʀ2)² - 4ʀ1ʀ2

= (9)² - 4 × 18 = 81 - 72 = 9

ᴛʜᴇʀᴇғᴏʀᴇ,

★ ʀ1 - ʀ2 = 3 ....→ (1)

★ ʀ1 + ʀ2 = 9....→ (2)

ᴀᴅᴅɪɴɢ (1) ᴀɴᴅ (2), 2ʀ1 = 12

=> ʀ1 = 6 Ω ᴀɴs.

ᴀɴᴅ

ʀ2 = 9 - 6 = 3 Ω ᴀɴs.

_________________________

$<marquee>❤í հօթҽ Եհís հҽlթs!❤$