Question

A parallel-plate air capacitor of area A = 13.7 cm² and plate separation of d = 2.90 mm is charged by a battery to a voltage of 71.0 V. What is the charge on the capacitor?

What is the capacitance of a parallel plate capacitor?

Answer 1

The charge on the capacitor is 39.83 µC and the capacitance is 63.41 pF.

Step-by-step explanation:

To find the charge on the capacitor, we can use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. From the formula, we can rewrite it as Q = AVd, where A is the area of the plates and d is the separation between the plates. Plugging in the given values, we have Q = (13.7 cm²) * (2.90 mm) = 39.83 µC.

To find the capacitance of a parallel plate capacitor, we can use the formula C = ε₀A/d, where C is the capacitance, ε₀ is the permittivity of free space, A is the area of the plates, and d is the separation between the plates. Plugging in the given values, we have C = (8.85 x 10^-12 F/m) * (13.7 cm² / (100 cm/m)²) / (2.90 mm / 1000 mm/m) = 63.41 pF.