Two coils, held in fixed positions, have a mutual inductance of m = 0.0034 h. the current in the first coil is i(t) = i0sin(ωt), where i0 = 5.4 a, ω = 143 rad/s.

m = 0.0034 h i0 = 5.4 a ω = 143 rad/s

(a) express the magnitude of the induced emf in the second coil, ε2, in terms of m and i.

(b) express the magnitude of ε2 in terms of m, io, and ω.

(c) express the maximum value of |ε2|, εmax, in terms of m, i0, and ω.

(d) calculate the numerical value of εmax in v.

Answer

given,

I(t) = I₀ sin(ωt),  

M = 0.0034 H, I₀ = 5.4 A,  ω = 143 rad/s.

a) magnitude of induced emf in terms of M and I

    ε₂ =

b) magnitude of induced emf in terms of M, Io, and ω

now,

      ε₂ =

c) maximum value of  |ε2|, εmax, in terms of M, I₀ , and ω.

       |ε₂| =

      for ε_{max} , cos ωt = 1

       ε_{max} =  

d) numerical value of εmax in V.

      ε_{max} =  

      ε_{max} =  

      ε_{max}  = 2.63 V

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get