A wire of uniform cross section and resistance 12 Ω is bent in the shape of a . . .

Question : A wire of uniform cross section and resistance 12 Ω is bent in the shape of a circle as shown. A resistance of 10 Ω is connected to diametrically opposite ends C and D. A battery of EMF 8 volt is connected between A and B. Determine the current flowing through the arm AD. 

Doubt by Ridhi 

CBSE Sample Question Paper 2023-2024

Solution : 

Total resistance of wire (R) = 12 Ω

R_AD=R_BD=[60°/360°]×12

=12/6
= 2Ω
R_AC=R_BC=[120°/360°]×12

=12/3
=4 Ω

Here the equivalent figure will be a balanced wheat stone bridge. Hence, no current will flow through 10Ω resistance. 

The equivalent circuit will look like the one as shown below 

Current through AD (I_AD) = Current through ADB (I_ADB)
I_AD=I_ADB=V/R_ADB
=8/4
= 2 A

Hence, the current flowing through the arm AD is 2 A.