Question

A solid, rectangular iron bar measures 0.30 cm by 3.0 cm by 25 cm .

Part A Find the resistance between opposing faces with crosssectional area 0.30 cm × 3.0 cm , assuming the faces in question are equipotentials. Express your answer using two significant figures.

R = ? Ω

Part B Find the resistance between opposing faces with crosssectional area 0.30 cm × 25 cm , assuming the faces in question are equipotentials.

R = ? Ω

Part C Find the resistance between opposing faces with crosssectional area 3.0 cm × 25 cm , assuming the faces in question are equipotentials.

R = ? Ω

Please write solutions and results. I will make rate if answers are right. Many thanks for all experts!

Answer 1

Part A:

Area of the opposing faces of the iron bar is

A = 0.30 cm × 3.0 cm

     = (0.30 cm²)(3 m / 100 cm)²

     = 0.90 x 10^-4 m²

Length of the iron bar

L = (25.0 cm)(1 m / 100 cm)

    = 25.0 x 10^-2 m

Specific resistance of the iron at room temperature is

= 1.00 x 10^-7 m

Now, the resistance of the iron bar is

R = L / A

    =(1.00 x 10^-7 m) (25.0 x 10^-2 m) / (0.90 x 10^-4 m²)

   = 2.77 x 10^-5

Therefore, the resistance between opposing faces with cross-sectional area 0.30 cm × 3.0 cm is 2.77 x 10^-4.

Part B:

Area of the opposing faces of the iron bar is

A = 0.30 cm × 25 cm

     = (7.5 cm²)(1 m / 100 cm)²

     = 7.5 x 10^-4 m²

Length of the iron bar

L = (3.0 cm)(1 m / 100 cm)

    = 3.0 x 10^-2 m

Specific resistance of the iron at room temperature is

= 1.00 x 10^-7 m

Now, the resistance of the iron bar is

R = L / A

    =(1.00 x 10^-7 m) (3.0 x 10^-2 m) / (7.5 x 10^-4 m²)

   = 4 x 10^-6

Therefore, the resistance between opposing faces with cross-sectional area 0.30 cm × 25 cm is 4 x 10^-6.

Part C:

Area of the opposing faces of the iron bar is

A = 3.0 cm × 25 cm

     = (75 cm²)(1 m / 100 cm)²

     = 75 x 10^-4 m²

Length of the iron bar

L = (0.30 cm)(1 m / 100 cm)

    = 0.30 x 10^-2 m

Specific resistance of the iron at room temperature is

= 1.00 x 10^-7 m

Now, the resistance of the iron bar is

R = L / A

    =(1.00 x 10^-7 m) (0.30 x 10^-2 m) / (75 x 10^-4 m²)

   = 4 x 10^-7

Therefore, the resistance between opposing faces with cross-sectional area 3.0 cm × 25 cm is 4 x 10^-7