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Capacitor and Capacitance
The document discusses capacitors and capacitance. It defines a capacitor as a device that stores electric potential energy and electric charge using two conductors separated by an insulator. It explains the concepts of capacitance, capacitors in series and parallel, and provides examples of calculating capacitance and stored energy for parallel plate capacitors.
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Capacitor and Capacitance
- 1. SIR JOHNEL V. ESPONILLA GENERALPHYSICS II
- 2. CAPACITORS AND CAPACITANCE CAPACITORS INSERIES AND PARALLEL EXAMPLE S
- 4. device that stores electricpotential energy and electric charge Two conductors separated by an insulator form a capacitor. The net charge on a capacitor is zero. To charge a capacitor, wires are connected to the opposite sides of a battery. This gives a fixed potential difference Vab = voltage of battery. CAPACITANCE: constant equal to the ratio of the charge on each conductor to the potential difference between them 𝑪 = 𝑸 𝑽𝒂𝒃 CAPACITANCE: Units: 1 Farad (F) = Q/V = C2/J = C2/Nm
- 5. PARALLEL PLATE CAPACITOR: Uniform electricfield between the plates, charge uniformly distributed over opposite surfaces 𝐸 = 𝑄 𝜀0𝐴 𝑉𝑎𝑏 = 𝐸 ∗ 𝑑 = 1 𝜀0 𝑄𝑑 𝐴 C= 𝑄 𝑉𝑎𝑏 = 𝜀0 𝐴 𝑑
- 6. CAPACITORS IN SERIES: Same charge(Q). 𝑉𝑎𝑏 = 𝑉 𝑎𝑐 + 𝑉𝑐𝑏 𝐶𝑒𝑞 = 𝑄 𝑉𝑎𝑏 = 𝑄 𝑉1 + 𝑉2 1 𝐶𝑒𝑞 = 𝑉1 𝑄 + 𝑉1 𝑄 = 1 𝐶1 + 1 𝐶2
- 7. CAPACITORS IN PARALLEL: Same potentialV, different charge. 𝑄1 = 𝐶1 𝑉1 𝑄2 = 𝐶2 𝑉2 𝑄 = 𝑄1 + 𝑄2 𝐶𝑒𝑞 = 𝑄 𝑉𝑎𝑏 = 𝑄1+𝑄2 𝑉 𝐶𝑒𝑞 = 𝑄1 𝑉 + 𝑄2 𝑉 = 𝐶1+ 𝐶2
- 8. Consider a parallel-platecapacitor that is about the size of your fingernail. The plates are squares with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air. a.) Find the capacitance. b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored? 𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 𝑼𝑵𝑲𝑵𝑶𝑾𝑵 𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹
- 9. Consider a parallel-platecapacitor that is about the size of your fingernail. The plates are squares with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air. a.) Find the capacitance. b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored? 𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 L = 1.0 cm or 0.010 m d = 10 𝜇m or 10 x 10-5 m 𝜀0 = 8.85 𝑥 10 − 12 C2/Nm2 UNKNOWN C
- 10. Consider a parallel-platecapacitor that is about the size of your fingernail. The plates are squares with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air. a.) Find the capacitance. b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored? 𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝐶 = 𝜀0 𝐴 𝑑 = 𝜀0 𝐿2 𝑑 C = (8.85 𝑥 10−12𝐶2 𝑁𝑚2 )(0.010𝑚)2 (1.0𝑥10−5𝑚) C = 8.9 x 10-11 F 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹
- 11. Consider a parallel-platecapacitor that is about the size of your fingernail. The plates are squares with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air. a.) Find the capacitance. b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored? 𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 C = 8.9 X 10-11 F ∆V = 12 V UNKNOWN PEcap
- 12. Consider a parallel-platecapacitor that is about the size of your fingernail. The plates are squares with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air. a.) Find the capacitance. b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored? 𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑃𝐸𝑐𝑎𝑝 = 1 2 𝐶(∆𝑉)2 𝑃𝐸𝑐𝑎𝑝 = 1 2 (8.9𝑥10−11 )(12𝑉)2 PEcap = 6.4 x 10-9 J 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹
- 13. Modern computer memoriesuse parallel-plate capacitors to store information, and these capacitors are the basic elements of a random- access memory (RAM) chip. Assume one of these capacitors has plates with area L x L, where L = 1.0 x 10-7m, and a plate separation d = 10 nm. a.) Find the capacitance of such a capacitor. b.) Calculate the amount of charge that must be placed onto the plates to obtain a potential difference of 5.0 V across them. c.) How many electrons does this charge correspond to? 𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 𝑼𝑵𝑲𝑵𝑶𝑾𝑵 𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹
- 14. Four capacitors areconnected. If all have the same capacitance (C1=C2=C3=C4=C), what is the equivalent capacitance of this combination? 𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 𝑼𝑵𝑲𝑵𝑶𝑾𝑵 𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹 C1 C2 C3 C4 C12=2C C34=2C Cequiv=C
- 15. 1. A voltageof 12 V is placed on a capacitor with C = 100 pF. a.) What is the charge on the capacitor? b.) How much energy is stored in the capacitor? 2. Two capacitors with C1=1.5𝜇F are connected in parallel. If the combined charge on both capacitors is 25 𝜇F, what is the voltage across the capacitor? 3. A parallel-plate capacitor has square plates of edge length 1.0 cm and a plate spacing of 0.10 mm. If the gap between the plates is filled with mica, what is the capacitance? 𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 𝑼𝑵𝑲𝑵𝑶𝑾𝑵 𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹