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MSTC Physics C

MSTC Physics C. Study Guide Chapter 20 Section 9. Energy Stored in a Capacitor. As a capacitor stores charge, it requires more work to move more charge to the capacitor because of the increased electric repulsion

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MSTC Physics C

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  1. MSTC Physics C Study Guide Chapter 20 Section 9

  2. Energy Stored in a Capacitor • As a capacitor stores charge, it requires more work to move more charge to the capacitor because of the increased electric repulsion • Work required to move a small amount of charge, dq, when there is a potential difference, V is dW = Vdq

  3. Energy Stored in a Capacitor • Total work done is W = ∫V dq • Since C = q/V W = ∫q/C dq =(1/2C) q2] = Q2 /2C • Energy stored in a capacitor is U = Q2/2C = ½ CV2 = ½ QV

  4. Sample Problem • A 12 V battery is connected to a 20 μF capacitor. How much electric energy can be stored in the capacitor?

  5. Energy Density • Consider a parallel plate capacitor when E field is uniform • Know E = V/d and C = εA/d • Since U = ½ CV2 = ½ (εA/d)(Ed)2 = ½ εE2Ad - Ad is the volume between the plates • So U/Ad = 1/2εE2Ad/Ad • Energy density = U/Volume = ½ εE2 • Electric energy stored per unit volume in any region of space is proportional to the square of the E field in that region

  6. Sample Problem • Two capacitors C1 and C2 are charged to the same potential difference Vo, but with opposite polarity. The charged capacitors are removed from the battery and their plates are connected. The switches S1 and S2 are then closed. A) Find the final potential difference between a and b after the switches are closed. B) Find the total energy stored in the capacitors before and after the switches are closed.

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