Apply the result of Problem 1 to find the resistance of a 10-cm-long hollow cylinder (Fig....

Apply the result of Problem 1 to find the resistance of a 10-cm-long hollow cylinder (Fig. 1) made of carbon with σ = 3 × 104 (S/m).

Problem 1

A coaxial resistor of length l consists of two concentric cylinders. The inner cylinder has radius a and is made of a material with conductivity σ1, and the outer cylinder, extending between r = a and r = b, is made of a material with conductivity σ2. If the two ends of the resistor are capped with conducting plates, show that the resistance between the two ends is R = l/[π(σ1a2+ σ2(b2− a2))].

Figure 1

Cross-section of hollow cylinder.