Question

a 1.0m long carbon pipe of inner diameter 3.0cm and outer diameter 5.0cm is cut in half lengthwise. determine the resistance between the inner surface and the outer surface of one of the half sections of pipe.

Answer 1

1.0m long carbon pipe of inner diameter 3.0cm and outer diameter 5.0cm is cut in half lengthwise hence,

the resistance between the inner surface and the outer surface of one of the half sections of the carbon pipe is 8.75 x 10^-6 Ω.

Step-by-step explanation:

In order to determine the resistance between the inner surface and the outer surface of one of the half sections of the carbon pipe, we need to calculate the resistance of a hollow cylinder.

The resistance of a hollow cylinder is given by the equation: R = (p * L) / (2π * (Ro - Ri)),

where R is the resistance, p is the resistivity, L is the length of the cylinder, Ro is the outer radius, and Ri is the inner radius.

Plugging in the values for the given carbon pipe: p = 3.5 x 10^-5 Ω*m, L = 0.5 m (since the pipe is cut in half lengthwise),

Ro = 2.5 cm

= 0.025 m,

and Ri = 1.5 cm

= 0.015 m,

we can calculate the resistance as follows:

R = (3.5 x 10^-5 Ω*m * 0.5 m) / (2π * (0.025 m - 0.015 m))

R = 8.75 x 10^-6 Ω

Answer 2

The resistance between the inner surface and the outer surface of one of the half sections of the pipe is 2.45 x 10^-4 Ω.

Step 1: Calculate the cross-sectional area of the pipe

The cross-sectional area of the pipe can be calculated using the formula for the area of a cylinder:

A = πr^2

where r is the radius of the pipe.

The inner radius of the pipe is 1.5 cm and the outer radius is 2.5 cm. Therefore, the cross-sectional area of the pipe is:

A = π(1.5 cm)^2 = 7.07 cm^2

Step 2: Calculate the resistivity of carbon.

The resistivity of carbon is 3.5 x 10^-5 Ωm.

Step 3: Calculate the length of the half section of pipe.

The length of the half section of pipe is 0.5 m.

Step 4: Calculate the resistance of the half section of pipe.

The resistance of the half section of pipe can be calculated using the formula for the resistance of a conductor:

R = ρl/A

where ρ is the resistivity of the conductor, l is the length of the conductor, and A is the cross-sectional area of the conductor.

Therefore, the resistance of the half section of pipe is:

R = (3.5 x 10^-5 Ωm)(0.5 m) / (7.07 cm^2) = 2.45 x 10^-4 Ω .