Question

An AC generator consists of eight turns of wire, each having area A =9.0x 10-2 m2, with a total resistance of 12.0 V. The coil rotates in a magnetic field of 0.500 T at a constant frequency of 60.0 Hz, with axis of rotation perpendicular to the direction of the magnetic field. (a) Find the maximum induced emf. [3] (b) What is the maximum induced current? [1] (c) Determine the induced emf and current as functions of time. [2] (d) Wiat maximum torque must be applied to keep the coil turning? (3)​

Answer 1

We have that the maximum induced emf,the maximum induced current, the induced emf and current as functions of time,The maximum torque must be applied to keep the coil turning are

a  )$E_{max}=135.6v$

b)  $I_max=11A$

c)  $I_i=11A sin(376.9rad/s t)$

   $E_i=135.6v sin(376.9rad/s )$

d)   $T=4.07Nm$

From the Question we are told that

Area $A =9.0x 10^{-2} m^2$

Total resistance of $R=12.0 V.$

Magnetic field of $B=0.500 T$

Constant frequency $F=60.0 Hz$

Eight turns $N=8N$

A)

Generally the equation for the maximum induced emf  is mathematically given as

$E=NAB\omega$

Where

$\omega=2\pi f$

$\omega=2*3.142*60$

$\omega=376.9rad/s$

$E_max=8*(9.0x 10-2)*0.5*376.9$

$E_{max}=135.6v$

B)

Generally the equation for the maximum induced Current is mathematically given as

$I_m=\frac{E}{R}\\\\I_max=\frac{135.6}{12}\\\\I_max=11A$

C)

Generally for the induced emf and current as functions of time we Substitute $E_{max}$ and $\omega$ into

$E_i=E_{max} sin\omega t$

$E_i=135.6v sin(376.9rad/s t)$

And Same for induces Current

$I_i=I_{max} sin\omega t$

$I_i=11A sin(376.9rad/s t)$

D)

Generally the equation for the  maximum torque  is mathematically given as

$T = rB sin θ$

Where

r= maximum magnetic moment

$r=NIAr= 8*11.3*0.090r=8.14m^2$

Therefore

$T = 8,14*0.500 sin 90$

$T=4.07Nm$

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