Answer to Question #167024 in Electric Circuits for Richard

Question

A cable has a resistance of 10.5 Ω. What will be the resistance of another cable of the same material twice as long and half the cross-section area?

Answer 1

Let $l_1$ - the length of the first cable;

$l_2=2l_1$ - the length of the second cable;

$A_1$ - the cross-sectional area of the first cable;

$A_2=A_1/2$ - the cross-sectional area of the second cable

$\rho$ - the resistivity of a material.

The resistance of the first cable is:

$R_1=\rho \frac{l_1} {A_1}.$

The resistance of the second cable is:

$R_2=\rho \frac{l_2}{A_2} =\rho\frac{2l_1}{\frac{A_1}{2}}=4R_1=4\cdot 10.5=42 \space Ohm.$

Answer: 42 Ohm.