c27p535e A cylindrical resistor of radius 54 mm and length 1

(c27p53_5e) A cylindrical resistor of radius 5.4 mm and length 1.7 cm is made of a material that has a resistivity of 3.50×10-5 m. What is the current density when the energy dissipation rate in the resistor is 1.0 W?

What is the potential difference?

Solution

radius r = 5.4*10^-3 m

So, area A = pi*r^2

length L = 0.017m

resistivity rho = 3.5*10^-5 ohm-m

We have the relation:

Resistance R = (rho*L)/A = (3.50×10-5 * 0.017)/(pi* (5.4*10^-3)^2) = 6.5*10^-3 ohm

Also given, P = 1W

I^2R = 1

I = sqrt(1/R) = 12.4 A

So, current density J = I/A = 12.4/(pi*(5.4*10^-3)^2) = 1.35*10^5 A/m^2

We know, P = VI

=> V = P/I = 1/12.4 = 0.0806 V