Question

A wire of resistance $4 \Omega$is used to wind a coil of radius 7 cm. The wire has a diameter of 1.4 mm and the specific resistance of its material is $2 \times 10 ^ { - 2 } \Omega$ m. The number of turns in the coil is

• A. 50
• B. 40
• C. 60
• D. 70

Answer 1

Answer: (D)

70

Answer 2

: Let n be the number of turns in the coil. Then total length of wire used, l

$= 2 \pi \mathrm { r } \times \mathrm { n } = 2 \pi \times 710 ^ { - 2 } \times \mathrm { n }$

Total resistance,

or , $4 = \frac { 2 \times 10 ^ { - 7 } \times 2 \pi \times 10 ^ { - 2 } \times n } { \pi \left( 0.7 \times 10 ^ { - 3 } \right) ^ { 2 } }$

$\therefore$ n = 70