The Capacitance and Potential Difference of a Cylinder Capacitor
Capacitance Calculation and Potential Difference
A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is 12.0 pC. The inner cylinder has a radius of 0.250 mm, the outer one has a radius of 5.00 mm, and the length of each cylinder is 22.0 cm.
1. What is the capacitance?
Using the formula for capacitance of a cylinder capacitor: C = (2πεo L) / ln(b/a), where εo = 8.854×10−12 F/m, we can calculate the capacitance:
C = (2π * 8.854×10−12 * 0.22) / ln(0.005 / 0.00025) = 17.65 * 10−12 F
2. What applied potential difference is necessary to produce these charges on the cylinders?
For this question, we need to find the potential difference using the formula: ΔV = Q/C
Substitute the values to find the potential difference:
ΔV = 12 * 10−12 / 17.65 * 10−12 = 0.68 V
Question:
What are the Capacitance and the Potential difference?
Question Parameter(s): the magnitude of the charge on each is 12.0 pC, the inner cylinder has a radius of 0.250 mm, and the outer one has a radius of 5.00 mm.
Answer:
1) The capacitance is 17.65 * 10−12 C/V
2) The applied potential difference needed is 0.68 V
Explanation: In order to calculate the capacitance of a cylinder capacitor, we used the given formula. By using the charge and radius values, we calculated the capacitance. The potential difference is then calculated using the obtained capacitance and charge value.