Question

A rectangular coil of N turns with length a and width b rotates at frequency fin a uniform magnetic field B. The coil is connected to co- rotating cylinders, against which metal brushes slide to make contact. Calculate the mathematical expression of the induced voltage. Sliding contacts вх х х х х х х х х х г 1 * x * Answer: 0 = NB · À = NabBcos(21ft) = V = -N = 21f NabBsin(2nft) Can you design a loop for the previous exercise that may produce 120 V with f = 60 Hz? Use a uniform magnetic field of 0.5 T. You should select sizes and number of turns after determining the value of the expression Nab.

Answer 1

Detailed solution is provided in below images :

Dragsumi X X sliding contacts X X X X X X X x x x x x x x - X X X X XVI- . х х х х fх (x x x xk x x x x x x x x - a - > X X X x B = Uniform magnetic field A = Area covered by loop = clob flua $ = B•A =BA Coswt. = BACOS 2016 | for N number of tuans $= N BACOS 2 Of A Voltage v= -ne | = - N ( Bfl cos2(tt) =-NBA C-sin(20ft))• 276 v= 27FNB A sin(27ft) v= 206NBub sinc2aft) CA=a.b) Now we have to put V= 120 Volt 60 Hz B- 0.5T Assume sincraft)= I So, 120 = 27 (60) NC0.5) ub:1) Nub = 0.63661

Value of product Nab = 0.63661.

Now we have to assume suitable value of N to obtain value of a and b.

Now assume that number of turns N= 25 then Nub= 0.63661 (25) alb= 0.63661 ab = 0.0254 6 Taking lu = 0.3 m (0.3) b = 0.02546 b = 0.0848 m

Note : You can select any suitable value for number of turns N. So you will get value of product ab. Then you have to select suitable value of a or b. After this you can get value of remaining variable.

Hope this answer will help you to solve your queries. Thank you!