Answer to Question #164384 in Electricity and Magnetism for global nina

Question

A capacitor is a device used to store electric charge. Typically, commercial capacitors have two conducting parts close to one another, separated by a significant gap. i. What is the capacitance of a parallel plate capacitor having plates of area 1.80 m2 that are separated by 0.05 mm of Pyrex glass (Dielectric constant=5.6)? ii. How much charge does it hold when 20.00 V is applied to it?

Answer 1

(i) The capacitance of the parallel-plate capacitor filled with dielectric can be written as follows:

$$C=\dfrac{\kappa\epsilon_0A}{d},$$ $$C=\dfrac{5.6\cdot8.85\cdot10^{-12}\ \dfrac{F}{m}\cdot 1.8\ m^2}{5\cdot10^{-5}\ m}=1.78\ \mu F.$$

(ii) We can find the amount of charge that the capacitor holds from the formula:

$$Q=C\Delta V=1.78\cdot10^{-6}\ F\cdot20\ V=35.6\ \mu C.$$