A ribbon of material with a rectangular cross sectional area of (0.25 mm x 1.00 mm), length 21.9 cm and resistance 1.5 is used as a heating element in a toaster. What is the resistivity of the material? a ) 1.31 × 10 − 6 Ω ⋅ m b ) 1.00 × 10 − 6 Ω ⋅ m c ) 1.71 × 10 − 6 Ω ⋅ m d ) 1.97 × 10 − 6 Ω ⋅ m e ) 1.50 × 10 − 6 Ω ⋅ m

Question

A ribbon of material with a rectangular cross sectional area of (0.25 mm x 1.00 mm), length 21.9 cm and resistance 1.5 is used as a heating element in a toaster. What is the resistivity of the material?  a  )  1.31  ×      10          −      6        Ω  ⋅  m    b  )  1.00  ×      10          −      6        Ω  ⋅  m    c  )  1.71  ×      10          −      6        Ω  ⋅  m    d  )  1.97  ×      10          −      6        Ω  ⋅  m    e  )  1.50  ×      10          −      6        Ω  ⋅  m

Bleha7s · Accepted Answer

The resistance of a material is proportional to  R  ∝      l    A      R  =            ρ      l        A       [  ρ  =  r  e  s  i  s  t  i  v  i  t  y  ]The expression for the resistivity of the material is  ρ  =            R      A        l  Here,   ρ is the resistivity, R is the resistance,  Ais the area of cross section, l is the length.in this case,  A  =  0.25     n  m  ⋅  1.00     m  m    I  =  21.9     c  m    R  =  1.5    ρ  =            (      1.5      Ω      )      (      (      0.25             m      m      ×      1.00             m      m      )      ×                        1          m                                      10            6                               m          m                    )              21.9             c      m      ×                        1                     m                          100                     c          m                        =  1.71  ×      10          −      6        Ω     mThus correct option is (c).

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