First term / second mid Exam [1433/ 1434] Q12. A conductor of radius I, length and resistivity p has resistance R. What is the new resistanc

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First term / second mid Exam [1433/ 1434] Q12. A conductor of radius I, length and resistivity p has resistance R. What is the new resistance if it is stretched to 4 times its original length?

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Kim Chi 6 months 2021-08-22T05:41:03+00:00 1 Answers 4 views 0

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    2021-08-22T05:42:31+00:00

    Answer:

    R’ = 4R

    Hence, the resistance increases to four times its initial value as well.

    Explanation:

    The resistance of a conductor in terms of its physical dimensions can be given by the following formula:

    R = \frac{\rho L}{A}\\  _______ equation (1)

    where,

    R = Resistance of the conductor

    ρ = resistivity of the material of the conductor

    L = Length of the conductor

    A = Cross-sectional Area of the conductor

    Now, if the length of the conductor is increased to four times, keeping other values constant, then:

    R' = \frac{\rho L'}{A}\\\\R' = \frac{\rho (4L)}{A}\\\\R' = 4\frac{\rho L}{A}

    using equation (1):

    R’ = 4R

    Hence, the resistance increases to four times its initial value as well.

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