A resistor is constructed of a carbon rod that has a uniform cross-sectional area of 5.10 mm2. When a potential difference of 12.0 V is appl

Question

A resistor is constructed of a carbon rod that has a uniform cross-sectional area of 5.10 mm2. When a potential difference of 12.0 V is applied across the ends of the rod, the rod carries a current of 4.40 ✕ 10-3 A.(a)What is the resistance of the rod?
(b) What is the rod’s length?

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Verity 4 years 2021-08-18T00:54:59+00:00 1 Answers 6 views 0

Answers ( )

  1. Amity
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    2021-08-18T00:56:09+00:00
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    Explanation:

    Given that,

    Area of cross section of the carbon rod, A=5.1\ mm^2=5.1\times 10^{-6}\ m^2

    Potential difference, V = 12 V

    Current, I=4.4\times 10^{-3}\ A

    (a) Let R is the resistance of the rod. Using Ohm’s law to find it as :

    V = IR

    R=\dfrac{V}{I}\\\\R=\dfrac{12}{4.4\times 10^{-3}}\\\\R=2727.27\ \Omega

    (b) The resistivity of carbon is,   \rho=3.5\times 10^{-5}\ \Omega-m

    The formula of resistance is given by :

    R=\rho\dfrac{L}{A}\\\\L=\dfrac{RA}{\rho}\\\\L=\dfrac{2727.27\times 5.1\times 10^{-6}}{3.5\times 10^{-5}}\\\\L=397.4\ m

    Hence, this is the required solution.

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