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

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.

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

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  1. Ch 17: Electrical Energy and Current17 -2: Capacitance

  2. 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.

  3. 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 unit of capacitance is the Farad: 1 F = 1C/V]

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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!

  12. _ _ _ + + + 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

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