A cylinder-shaped carbon resistor is 8 cm in length and its circular cross section has a diameter d = 1 mm.
(a) Determine the resistance R.
(b) To reduce its resistance by 40%, the carbon resistor is coated with a layer of copper of thickness t. Use the result of Problem to determine coaxial resistor of length / consists of two concentric cylinders. The inner cylinder has radius a and is made of a material with conductivity, σ1 and a the outer cylinder, extending between r = a and r = b, is made of a material with conductivity an. 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)].
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