Capacitors and Capacitance: Calculating Charge, Energy, and Equivalent Capacitance
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Capacitor and Capacitance; their definition, formulae, and examples
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Capacitors and Capacitance: Calculating Charge, Energy, and Equivalent Capacitance
- 1. SIR JOHNEL V. ESPONILLA GENERAL PHYSICS II
- 2. CAPACITORS AND CAPACITANCE CAPACITORS IN SERIES AND PARALLEL EXAMPLE S
- 4. device that stores electric potential 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 electric field 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 potential V, 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-plate capacitor 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-plate capacitor 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-plate capacitor 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-plate capacitor 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-plate capacitor 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 memories use 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 are connected. 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 voltage of 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