Ch 17: Electrical Energy and Current 17 -2: Capacitance

A capacitor is a device whose purpose is to store electrical energy which can then be released in a controlled manner during a short period of time. A capacitor consists of 2 spatially separated conductors which can be charged to +Q and -Q respectively.

Q = magnitude of charge on the plates V = potential difference The capacitance is defined as the ratio of the charge on one conductor of the capacitor to the potential difference between the conductors. C = capacitance Q = magnitude of charge on the plates V = potential difference The capacitance belongs only to the capacitor, independent of the charge and voltage. [The unit of capacitance is the Farad: 1 F = 1C/V]

° = permittivity of free space = constant ° = 8.85 x 10-12 C2/N•m2 Capacitance is a measure of the conductor’s ability to store charge, it depends on the geometry of the capacitor. C = ° A d ° = permittivity of free space = constant ° = 8.85 x 10-12 C2/N•m2 Capacitance for a parallel plate capacitor in a vacuum

Parallel Plate Capacitor The device consists of plates of positive and negative charge The total electric field between the plates is given by The field outside the plates is zero

Capacitor with a Dielectric A dielectric is an insulating material inserted between the plates to increase capacitance. New capacitance given by: C = K Co K = dielectric constant Co = capacitance in a vacuum

Sample Problem An empty parallel plate capacitor, Co = 25 mF is charged with a 12 V battery. The battery is disconnected and the region between the plates is filled with water. Find the capacitance, charge and voltage of the water-filled capacitor. Given: Co = 25 mF Vo = 12 V

Co = ° A = 25 mF d the geometry of the plates doesn’t change so, C = KCo = 80 (25 x 10-6 F) = 2.0 x 10-3 F

Since the battery is disconnected, the charge on the plates stays the same Q = CoVo = (25 x 10-6 F)(12V) = 3.0 x 10-4 C

The new voltage is given by: q = CV  V= q/C =. 3. 0 x 10– 4 C. 2 The new voltage is given by: q = CV  V= q/C = 3.0 x 10– 4 C 2.0 x 10-3 F = 0.15 V

Energy stored in a capacitor The energy stored in the field can be found by: PE = ½ qV Since q = CV PE = ½ CV2 equivalently PE = q2 2C Note: E here stands for energy, measured in Joules, Not electric field!

Lightning (the atmosphere is a BIG capacitor!!) _ + Collisions produce charged particles. The heavier particles (-) sit near the bottom of the cloud; the lighter particles (+) near the top. Stepped Leader Negatively charged electrons begin zigzagging downward. Attraction As the stepped leader nears the ground, it draws a streamer of positive charge upward. Flowing Charge As the leader and the streamer come together, powerful electric current begins flowing Contact! Intense wave of positive charge, a “return stroke,” travels upward at 108 m/s