Question

Three resistors are made out of three different materials and have different (but uniform) cross sections. Resistor 1 has a circular cross section of radius 2.47 mm . Resistor 2 has a square cross section with a side length of 3.07 mm . The third resistor's cross section is a right triangle with two sides of length 6.47 mm . All of the resistors are 0.763 cm in length. Use the provided table of resistivities to calculate the resistance of each resistor.

Material 1 0.00591 Ω⋅m

Material 2 0.488 Ω⋅m

Material 3 4.63×10−5 Ω⋅m

Three shapes, numbered 1 to 3. Shape one is a circle. Shape 2 is a square. Shape 3 is a right triangle. ?1= Ω ?2= Ω

?3= Ω

Answer 1

For R1 (circular cross-section) :

l = length = 0.763 cm = 0.00763 m

r = radius = 2.47 mm = 0.00247 m

rho = 0.00591 Ω⋅m

resistance R1 = [answer]

For R2 (square cross-section):

l = length = 0.763 cm = 0.00763 m

L = side length = 3.07 mm = 0.00307 m

rho = 0.488 Ω⋅m

reistance R2 = [answer]

For R3 (triangular cross-section):

l = length = 0.763 cm = 0.00763 m

b = base = h = height = 6.47 mm = 0.00647 m

rho = 4.63×10−5 Ω⋅m

resistance R3 = [answer]