Question

A generator has a square coil consisting of 248 turns. The coil rotates at a rate of 755.35 rev/min in a 0.170 T magnetic field. The maximum value of emf generated is 75 V. What is the length of one side of the coil

Answer 1

Answer:

The length of one side of the coil is 0.15 m.

Explanation:

Given;

number of turns, N = 248 turns

angular velocity, ω = 755.35 rev/min

angular velocity, ω (in rad/s) =  755.35 rev/min x 2π/60 s = 79.1 rad/s

magnetic field strength, B = 0.170 T

maximum value of emf generated, ξ₀ = 75 V

Maximum emf induced in the coil is given as;

ξ₀ = NABω

where;

A is the area of the square coil

A = ξ₀ / NBω

A = 75 / ( 248 x 0.17 x 79.1)

A = 0.0225 m²

Area of square = L x L = L²

L² =  0.0225 m²

L = √ 0.0225

L = 0.15 m

Therefore, the length of one side of the coil is 0.15 m.

Answer 2

Answer:

the length of one side of the coil is 0.15 m

Explanation:

Given that,

no of turn = 2648

coil rotates = 755.35rev/min

(in rad/s) =  755.35 rev/min x 2π/60 s = 79.1 rad/s

magnetic field = 0.170 T

maximum value of emf generated is 75 V

we will apply here formula for maximum emf induced in a coil that is

εo = N × A × B × ω  

Area A = l²

so

$l = \sqrt{A}$

$I = \sqrt{\frac{\epsilon _o}{N\times B\times \omega} }$

Substitute the value the the formula above

$l = \sqrt{\frac{75}{248\times 0.170\times 79.10}}\\\\l = 0.14997m\\\\\approx0.15m$

Thus, the length of one side of the coil is 0.15 m.