A1.70 m cylindrical rod of diameter 0.550 cm is connected to a power supply that maintains a constant potential difference of 13.0 v across its ends, while an ammeter measures the current through it. you observe that at room temperature (20.0∘c) the ammeter reads 18.7 a, while at 92.0∘c it reads 17.1 a. you can ignore any thermal expansion of the rod. 1.find the resistivity and for the material of the rod at 20 ^\circ {\rm c}. (rho= ? ω*m)

2.find the temperature coefficient of resistivity at 20 ^\circ {\rm c} for the material of the rod.(α= ? (c)^-1)

ρ(20°C) = 9.7 * 10^-6 Ω m

α = 0.0013 /°C

Explanation:

Step 1: Data given

length of the rod = 1.70 meters

diameter = 0.55 cm

Potential difference = 13.0 V

Temperature = 20°C →18.7 A

At 92°C → 17.1 A

Step 2: Calculate the resistivity

ρ =  (RA)/L

 ⇒ with R = the resistance of the rod

   ⇒ R = V/I0 = 13/18.7 = 0.695 Ω

 ⇒ with L = length in meters  = 1.70 m

 ⇒ with A = cross sectional area in m^2  =  π * r²  

    ⇒ r = d/2 = 0.550/2 = 0.275 cm = 0.00275m

ρ(20°C) = (R*π * r²  )/L

ρ(20°C) = (0.695 * π 0.00275²)/1.7

ρ(20°C) = 9.7 * 10^-6 Ω m

ρ(92°C) = (R*π * r²  )/L

  ⇒ R = 13/17.1 = 0.76

ρ(92°C) =(0.76 * π 0.00275²)/1.7

ρ(92°C) = 1.06 *10^-5 Ω m

2.Find the temperature coefficient of resistivity at 20 ^\circ {\rm C} for the material of the rod.(α= ? (C)^-

RT = R0*[1 + α(T-T0)]

⇒ with RT = the resistance of the rod at tmperature T = 92.0°C

⇒ with R0= the resistance of the rod at temperature T = 20°C

⇒ with α = the temperature coefficient of resisivity

⇒ with T = 92°C

⇒ with t0 = 20°C

RT = V/I = 13.0/ 17.1 =0.76 Ω

α =((RT/R0)-1)/(T-T0)

α = ((0.76/0.695)-1)/(92-20)

α = 0.0013 /°C

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft

the components of a vector are the parts of the vectors that are to each other.

b perpendicular