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GENERAL PHYSICS LECTURE Chapter 26 CAPACITANCE AND DIELECTRICS PhD: Nguyễn Thị Ngọc Nữ ELECTRIC POTENTIAL CAPACITANCE AND DIELECTRICS A capacitor consists of two conductors carrying charges of equal magnitude and opposite sign. The conductors are called plates. CAPACITANCE AND DIELECTRICS CAPACITANCE AND DIELECTRICS + - A B CAPACITANCE AND DIELECTRICS + + + + + + + + + DV1 Q1 + + + + + + + … DVn = nDV1 Qn= n Q1 DV2 = 2DV1 Q 2= 2 Q 1 Q1 DV Q2 D V2 Qn D Vn CAPACITANCE AND DIELECTRICS The capacitance C of any capacitor is the ratio of the charge Q on either conductor to the potential difference DV between them: C Q DV The SI unit of capacitance is the farad (F). 1 F=1 C/V. CAPACITANCE AND DIELECTRICS Quick Quiz A capacitor stores charge Q at a potential difference DV. If the voltage applied by a battery to the capacitor is doubled to 2DV, (a) the capacitance falls to half its initial value and the charge remains the same (b) the capacitance and the charge both fall to half their initial values (c) the capacitance and the charge both double (d) the capacitance remains the same and the charge doubles. CAPACITANCE AND DIELECTRICS Capacitance of an isolated charged sphere C Q DV R ke Parallel-Plate Capacitors C Q DV 0A d CAPACITANCE AND DIELECTRICS Quick Quiz Many computer keyboard buttons are constructed of capacitors, as shown in Figure 26.5. When a key is pushed down, the soft insulator between the movable plate and the fixed plate is compressed. When the key is pressed, the capacitance (a) increases, (b) decreases, or (c) changes in a way that we cannot determine because the complicated electric circuit connected to the keyboard button may cause a change in DV. CAPACITANCE AND DIELECTRICS Quick Quiz Figure 26.5. CAPACITANCE AND DIELECTRICS Problem 1 An isolated charged conducting sphere of radius 12.0 cm creates an electric field of 4.90 x 104 N/C at a distance 21.0 cm from its center. (a) What is its surface charge density? (b) What is its capacitance? CAPACITANCE AND DIELECTRICS Problem 2 An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2, separated by a distance of 1.80 mm. A 20.0-V potential difference is applied to these plates. Calculate (a) the electric field between the plates, (b) the surface charge density, (c) the capacitance, and (d) the charge on each plate. CAPACITANCE AND DIELECTRICS CAPACITANCE AND DIELECTRICS CAPACITANCE AND DIELECTRICS Series combination CAPACITANCE AND DIELECTRICS Parallel combination CAPACITANCE AND DIELECTRICS Series combination Parallel combination D V D V1 D V 2 ... D V D V1 D V 2 Q Q 1 Q Q Q 1 Q 2 ... 1 C eq 1 C1 2 ... 1 C2 ... C eq C 1 C 2 ... CAPACITANCE AND DIELECTRICS Quick Quiz 1 Two capacitors are identical. They can be connected in series or in parallel. If you want the smallest equivalent capacitance for the combination, do you connect them in (a) series, in (b) parallel, or (c) do the combinations have the same capacitance? CAPACITANCE AND DIELECTRICS Quick Quiz 2 Two capacitors are identical. They can be connected in series or in parallel. Each capacitor is charged to a voltage of 10 V. If you want the largest combined potential difference across the combination, do you connect them in (a) series, in (b) parallel, or (c) do the combinations have the same potential difference? CAPACITANCE AND DIELECTRICS Problem 1 Two capacitors, C1= 5.00 mF and C2 = 12.0 mF, are connected in parallel, and the resulting combination is connected to a 9.00-V battery. (a) What is the equivalent capacitance of the combination? What are (b) the potential difference across each capacitor and (c) the charge stored on each capacitor? CAPACITANCE AND DIELECTRICS Problem 2 Evaluate the equivalent capacitance of the configuration shown in Figure. All the capacitors are identical, and each has capacitance C. CAPACITANCE AND DIELECTRICS W 1 Q 2 2 C 1 CDV 2 2 2 Energy density uE 1 2 oE 1 2 QDV CAPACITANCE AND DIELECTRICS Quick Quiz 1 You have three capacitors and a battery. In which of the following combinations of the three capacitors will the maximum possible energy be stored when the combination is attached to the battery? (a) series (b) parallel (c) Both combinations will store the same amount of energy. CAPACITANCE AND DIELECTRICS Quick Quiz 2 You charge a parallel-plate capacitor, remove it from the battery, and prevent the wires connected to the plates from touching each other. When you pull the plates apart to a larger separation, do the following quantities increase, decrease, or stay the same? (a) C; (b) Q; (c) E between the plates; (d) DV ; (e) energy stored in the capacitor.