CGPET 2021 Solved Paper

Given, effective resistance between points A and D,
RAD=3Ω
The circuit is shown as

Resistance of sides AC and CB are in series
∴ R1=3+3=6Ω.....(i)
Resistance R1 and R are in paralel

∴

1

R2

=

1

R

+

1

R1

⇒ R2=

R.R1

R+R1

.....(ii)
Resistance of sides AB and BD are series,

R3=R2+3 ....(iii)
Now, resistance R3 and 3Ω are parallel

∴ R4=

R3×3

R3+3

.......(iv)
Put the value from Eqs. (i), (ii) and (iii) in Eqs. (iv), we get
R4=

(R2+3)3

(R2+3)+3

=

3R2+9

R2+6

=

3( RR1 R+R1 )+9

( RR1 R+R1 )+6

⇒ 3=

( 6R R +6)+9

( 6R R +6)+6

(Given,R4=RAD=3Ω)
⇒R=6Ω