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summary. Capacitance Parallel plates, coaxial cables, Earth Series and parallel combinations Energy in a capacitor Dielectrics Dielectric strength. (25 - 12). Series combinations reduce the capacitance. Equal C reduce by the number involved. In parallel the capacitance increases.

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  1. summary • Capacitance • Parallel plates, coaxial cables, Earth • Series and parallel combinations • Energy in a capacitor • Dielectrics • Dielectric strength

  2. (25 - 12)

  3. Series combinations reduce the capacitance. Equal C reduce by the number involved. • In parallel the capacitance increases. • A basket of 4 capacitors, each of C = 6 nF. How can you arrange them to get • 1.5 nF • 2 nF g) 2.4 nF • 3 nF h) 3.6 nF • 4 nFi) 4.5 nF j) 6 nF • 12 nF k) 18 nF • 24 nF

  4. clicker All C’s are 8.00 nF. The battery is 12 V. What is the equivalent capacitance? 4 nF 6 nF 8 nF 10 nF 12 nF

  5. All C’s are 8.00 nF. The battery is 12 V. What is the equivalent capacitance? • C12 = 4 nF • C123 = 12 nF • Q123 = C123 x V = 144 nC • Q3 = C3 x V = 96 nC • Q12 = C12 x V = 48 nC • U123 = ½ C123V2 = ½ x 12x10-9 x122 = 864 nJ • U1 = ½ C1V12 = ½ x 8x10-9 x62 = 144 nJ = U2 • U3 = ½ x 8x10-9 x122 = 576 nF • C3 stores most energy, also the highest electric field and most charge, the most stressed part of the circuit.

  6. Circuits • All capacitors being the same, rank the equivalent capacitances of the four circuits.

  7. C1 = C3 = 8.00 μF, C2 = C4 = 6.00 μF, V = 12V When the switch S is closed, how much charge flows through point P C123 2.4 µF, q = 28.8 µC C2C24 = 12 µF C1234 = 3 µF q =36 µC Δq = 7.2 µC

  8. q V -q q' V -q' V q -q V' q -q (25 - 15)

  9. q V -q q' V -q' V q -q V' q -q (25 - 16)

  10. If the areas are A1 and A-A1. Effect of a dielectric : C  κC C123 2.4 µF, q = 28.8 µC C2C24 = 12 µF C1234 = 3 µF q =36 µC

  11. The force on a filling dielectric as it is inserted between the parallel plates of a capacitor. x L With the battery connected, U1 = ½CV2 With the battery disconnected, U2 = Q2/2C With the battery connected, since x is increasing downwards, a negative force is upwards, pushing the dielectric away. With the battery disconnected, the force is positive and pointed downwards, pulling in the dielectric. The force is proportional to (κ-1) and inversely to L.

  12. A question • What is the equivalent capacitance between the points A and B? • 1 μF • B. 2 μF • 4 μF • 10μF • None of these A B What would a 10V battery do, i.e. how much charge will it provide, when it is connected across A and B? 40 μC

  13. Question • A parallel-plate capacitor has a plate area of 0.3m2 and a plate separation of 0.1mm. If the charge on each plate has a magnitude of 5x10-6 C then the force exerted by one plate on the other has a magnitude of about: • 0 • 5N • 0. 9N • 1 x104 N • 9 x 105 N The electric field = σ/2εo why?

  14. Question • A parallel-plate capacitor has a plate area of 0.3m2 and a plate separation of 0.1mm. If the charge on each plate has a magnitude of 5x10-6 C then the force exerted by one plate on the other has a magnitude of about: • A. 0 B. 5N C. 9N D. 1 x104 N E. 9 x 105 N

  15. A question • Each of the four capacitors shown is 500 μF. The voltmeter reads 1000V. The magnitude of the charge, in coulombs, on each capacitor plate is: A. 0.2 B. 0.5 C. 20 D. 50 E. none of these

  16. HITT A parallel-plate capacitor has a plate area of 0.2m2 and a plate separation of 0.1 mm. To obtain an electric field of 2.0 x 106 V/m between the plates, the magnitude of the charge on each plate should be: A. 8.9 x 10-7 C B. 1.8 x 10-6 C C. 3.5 x 10-6 C D. 7.1 x 10-6 C E. 1.4 x 10-5 C

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