Map Sapling Learning Three resistors are made out of three different materials a

Question

Map Sapling Learning 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 2.90 mm. Resistor 2 has a square cross section with a side length of 5.62 mm. The third resistor's cross-section is a right triangle with two sides of length 4.53 mm as shown. All of the resistors are 0.688 cm in length. Use the provided table of resistivities to calculate the resistance of each resistor. Material 1 9.27 x 103 Q.m 0.779 m Material 2 Number Material 3 9.11 x 1050 m R, 2.41 Number 2.90 mm 113.5 5.62 mm Number 3 4.53 mm Incorrect Previous Give Up & View solution Try Again Next Ext Explanation

Explanation / Answer

Resistance = R = rho*(L/A)

A1 = pi*r^2 = pi*(2.9*10^-3)^2 = 2.64*10^-5 m^2

A2 = a^2 = (5.62*10^-3)^2 = 3.2*10^-5 m^2

A3 = ab/2 = (4.53*10^-3)^2/2 = 1.03*10^-5 m^2

Now R1 = 9.27*10^-3*(0.688*10^-2/2.64*10^-5) = 2.41 ohm

R2 = 0.779*(0.688*10^-2/3.2*10^-5) = 167.485 ohm

R3 = 9.11*10^-5*(0.688*10^-2/1.03*10^-5) = 0.06085 ohm

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