Answer to Question #319010 in Electric Circuits for Leo

Question

1. Calculate the resistance of a copper wire that is 3-meter long and has a diameter of 0.005m.

2. The resistance of a piece of carbon at 20⁰C is 10 Ω. What is its resistance at (a) 30⁰C &(b) 10⁰C?

providing the given, required, formula, solution/substitution of data,

Answer 1

1. Given:

l = 3 m,

d = 0.005 m,

$\rho=1.7\cdot 10^{-8} Ohm\cdot m.$

Required:

R - ?

Solution:

$R=\rho\frac{l} {S} =\rho\frac{4l} {\pi d^2}=1.7\cdot 10^{-8}\cdot \frac{4\cdot 3} {3.14\cdot 0.005^2}=0.0026\space Ohm.$

2.

Given:

$R_{0}= 10\space Ohm,$

$\alpha=-0.0005\space 1/\degree C,$

$t_0=20 \degree C,$

$t_1=30 \degree C,$

$t_2=10 \degree C.$

Required:

$R_1$ - ?

$R_2$ - ?

Solution:

$R_1=R_0(1+\alpha(t_1-t_0))=10(1+(-0.0005)(30-20))=9.95\space Ohm.$

$R_2=R_0(1+\alpha(t_2-t_0))=10(1+(-0.0005)(10-20))=10.05\space Ohm.$