Question

The resistance, R (in ohms), of a wire varies

directly with the length, L (in cm), of the
wire, and inversely with the cross-sectional
area, A (in cm2). A 500 cm piece of wire with
a radius of 0.2 cm has a resistance of 0.025
ohm. Find an equation that relates these
variables.

Answer 1

R ∝ L/ A

R = K L/ A

0.025= 500K/0.126

the constant, K=6.3 X 10^-6

Explanation:

Step 1

The resistance, R (in ohms), of a wire varies directly with the length, L (in cm), of the wire, and inversely with the cross-sectional

area, A (in cm2) is written mathematically as

R ∝ L/ A

Introducing the constant of proportionality,K, we have

R = K L/ A

So given that s 500 cm piece of wire with a radius of 0.2 cm has a resistance of 0.025 ohm.

We would First find area , since radius was given

Area = πr²

= 3.142 x 0.2²= 0.126cm²

Step 2

With our equation , R = K L/ A, puting all the necessary variables, we have

R = K L/ A

0.025= 500K/0.126

Solving for K

0.025= 500K/ 0.126

(0.025 X 0.126)/500 = K

K=6.3 X 10^-6

Answer 2

The equation is:
`R = (L)/(A)`

Explanation:

The resistance, R (in ohms), of a wire varies directly with the length, L (in cm), of the wire, and inversely with the cross-sectional area, A (in cm2).

This means that we want to find an equation for R, which is a fraction.

Since it varies directly with the length L, L is the numerator.

Since it varies inversely with the cross-sectional area, A is the denominator.

So the equation is:

`R = (L)/(A)`