The device pictured at the right consists of two solid cylinders of conducting m
ID: 1600787 • Letter: T
Question
The device pictured at the right consists of two solid cylinders of conducting material: a piece of tungsten (W) and a piece of iron (Fe), both of length l = 5.0 cm. The area of the flat ends is 0.050 cm^2. A 1.5 V ideal battery is connected between the flat ends of this device so that current flows through it. The resistivities (at the operating temperature) for these materials are rho_w = 5.6 times 10^-8 Ohm middot m and rho_Fe = 10.0 times 10^-8 Ohm middot m. (a) What current density flows in this device? (b) What electric field exists inside the iron piece? (c) What total power is dissipated as heat by this device?Explanation / Answer
a) total resistance, R = Rw + RFe
= rho_W*L/A + rho_Fe*L/A
= 5.6*10^-8*0.05/(0.05*10^-4) + 10*10^-8*0.05/(0.05*10^-4)
= 1.56*10^-3 ohms
current through the device, I = V/R
= 1.5/(1.56*10^-3)
= 961.5 A
Current density, J = I/A
= 961.5/(0.05*10^-4)
= 1.92*10^8 A/m^2
b) use,
E_Fe = J*rho_Fe
= 1.92*10^8*10*10^-8
= 19.2 N/c
c) Power dissipated, P = V^2/R
= 1.5^2/(1.56*10^-3)
= 1442 W