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L13_Viet_Capacitance and Capacitors

# L13_Viet_Capacitance and Capacitors - Physics 122B...

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Physics 122B Electricity and Magnetism Lecture 13 Capacitance and Capacitors

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05/13/09 Physics 122 - Lecture 13 2 Combining Capacitors Parallel: Same V, but different Qs. Series: Same Q, but different Vs. 1 2 3 parallel C C 1 2 3 Q Q Q Q C V V C C C + + + = = = + + + L L ( 29 ( 29 ( 29 series C 1 2 3 1 2 3 1 2 3 1 2 3 1 / / / 1 || || || 1/ 1/ 1/ Q Q C V V V V V Q V Q V Q C C C C C C = = + ∆ + ∆ + = + ∆ + ∆ + = + + + L L L L
05/13/09 Physics 122 - Lecture 13 3 Reminder: Combining Resistors R net 1 2 3 Series Connection [ L]: net R R R R Σ = + + 1 2 3 Parallel Connection [ (1/A)]: 1 1 1 1 net R R R R Σ = + + R net I Conducting material that carries current across its length can form a resistor , a circuit element characterized by an electrical resistance R: R ρ L/A where L is the length of the conductor and A is its cross sectional area. R has units of ohms . Multiple resistors may be combined in series , where resistances add, or in parallel , where inverse resistances add.

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05/13/09 Physics 122 - Lecture 13 4 Example : A Capacitor Circuit Find the charge and potential difference across each capacitor shown in the figure. C Q C V C parallel 1 2 C C C = + 1 2 series 1 2 1 2 1 1/ 1/ C C C C C C C = = + +
05/13/09 Physics 122 - Lecture 13 5 Energy Stored in a Capacitor 1 U dq V qdq C = = 2 1 C 2 0 1 Q Q U qdq C C = = 2 1 1 2 C C 2 2 Q U C V C = =

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05/13/09 Physics 122 - Lecture 13 6 Example : Storing Energy in Capacitor How much energy is stored in a 2.0 μ F capacitor that has been charged to 5000 V? What is the average power dissipation if the capacitor is discharged in 10 μ s? 2.0 μ F 5 kV 1 1 2 -6 2 C 2 2 (2.0 10 F)(5000 V) 25 J U C V = = = 6 5 (25 J) 2.5 10 W 2.5 MW (1.0 10 s) U P t - = = = =
05/13/09 Physics 122 - Lecture 13 7 Energy in the Electric Field ( 29 ( 29 2 1 1 2 2 0 0 C 2 2 2 A U C V Ed Ad E d ε ε = = = 2 C 0 E energy stored storage volume 2 U u E Ad ε = = Example: d=1.0 mm,

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