TG EAMCET 3 May 2025 Shift 2 Paper

Step 1: Total length of the wire
The total length of the wire is the length of the semicircle plus the diameter. That is:
l=πR+2R
Step 2: Find resistance per unit length
Since the total resistance is 36Ω for the entire wire, resistance per unit length is:
σ=‌

36

πR+2R

Step 3: Resistance along the diameter (straight part)
The length of the diameter is 2R. So, resistance along the diameter is:
R1=σ×2R=‌

36

πR+2R

×2R=‌

72

π+2

Step 4: Resistance along the semicircle
The length of the semicircle is πR. So, resistance along the semicircle is:
R2=σ×πR=‌

36

πR+2R

×πR=‌

36π

π+2

Step 5: Connect the two paths in parallel
The diameter and semicircular parts connect at both ends, so they are in parallel. Use the formula for parallel resistances:
Req=‌

R1R2

R1+R2

Step 6: Substitute the values for R1 and R2
Req=‌

‌ 72 π+2 × 36π π+2

72 π+2 +‌ 36π π+2

=‌

72×36π

(π+2)(36π+72)

Step 7: Simplify the expression further
=‌

72×36×22×7

36×(36×22+72×7)

=‌

72×22×7

36(22+14)

=‌

77

9

Ω