the wire used in arrangement shown in figure has a resistance r ohm per meter find the equivalent resistance - Science - Electricity

Question

the wire used in arrangement shown in figure has a resistance r ohm
per meter find the equivalent resistance between point A and B if
radius of circle is 1cm

Vipra Mishra · Accepted Answer

Dear Student

The given figure can be redrawn as
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_576112d4b39ec%20png"
style="width: 149px; height: 142px;">
Resistance R1, R2 and R3 are
connected in parallel

Value of resistance can be calculated as
Resistance of wire R = resitance per unit length ×length R1 =r×2πradius4  (As length of R1 is equal to quarter of circle circumference)R1 =r×2π14=πr2R2 =(r+r)radius  (As length of R2 is equal to 2 times of radius)R2 =(r+r)1 =2rR3 =r×3×2πradius4  (As length of R1 is equal to 3/4 of circle circumference)R3 =r×3×2π14=3πr2So1R=1R1+1R2+1R31R=2πr+12r+23πr=12+3π+46πr=16+3π6πrR =6πr16+3π

Regards

the wire used in arrangement shown in figure has a resistance r ohm per meter. find the equivalent resistance between point A and B if radius of circle is 1cm