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Question
If ρ is the specific resistance of a conductor of length ‘l’, area of cross-section ‘a’ and resistance ‘R’, what is the relationship between ρ, l, a and R?
Short Answer
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Solution
The resistance of a conductor is directly proportional to its length and inversely proportional to its area of cross-section. Therefore,
\[R = \rho\frac{l}{a}\]
Equivalently, the specific resistance is
\[\rho = \frac{Ra}{l}\]
Thus, resistance equals specific resistance multiplied by the length of the conductor and divided by its area of cross-section.
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