The resistance of a very fine aluminum wire with a 20 μm × 20 μm square cross section is 1200 Ω . A 1200 Ω resistor is made by wrapping this wire in a spiral around a 2.3-mm-diameter glass core. How many turns of wire are needed?

Explanation:

The given data is as follows.

         Resistance (R) = 1200 ohm,     Area (A) = m (as )

            Diameter (d) = 2.3 mm = m

First, we will calculate the length as follows.

            R =

Here,   = resistivity of aluminium =

Putting the given values above and we will calculate the value of length as follows.

               R =

             1200 =

               L =

As the circumference of circular wire =

or,                                                          =  

                                                              =

And, number of turns will be calculated as follows.

             No. of turns × Circumference = Length of wire

              No. of turns ×

                               =

Thus, we can conclude that  turns of wire are needed.

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