A wire of given material having length l and area of cross section A has a resistance of 4ohm. What would be the resistance of another wire of the same material having length l/2 and area of cross section 2A???
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Given :
- Length = l
- Area of cross section = A
- Resistance =
- Length =
- Area of cross section =
To find :
- Resistance of second wire.
Formula to be used :
where,
- = resistivity of the material
- l = length of the wire
- A = Area of cross section of wire
Solution :
Resistance of first wire -
-- [ given ]
Let --
Resistance of second wire -
Substituting the given values for second wire
Converting division into multiplication
Proceeding with simple calculation
Substituting the value of ρl/A from 1
______________________
Henceforth,
❒ The resistance of the second wire is
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