Energy and Capacitors Remember that the voltage V is the work done per unit charge: Imagine the capacitor is partially charged so that the charge on the.

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Presentation transcript:

Energy and Capacitors Remember that the voltage V is the work done per unit charge: Imagine the capacitor is partially charged so that the charge on the plates is Q It then acquires a little more charge δQ. This involves the work of moving charge δQ from one plate to the other. If δQ is very small V can be considered unchanged in which case Q+ δQ Q + + + + + V - - - - - C

Energy and Capacitors And as Q+ δQ + + + + + V - - - - - C We can substitute for V C So the total work done in giving the capacitor full charge from 0 to Qfull And in the limit as δQ→0

Writing Q fpr Qfull and making use of Q=VC similarly W =the energy stored by the charged capacitor (J) Q= the charge on the plates (C) V= the pd across the plates (V) C = the capacitance of the capacitor (F)

Q=VC implies that graphs of Q against V must be straight line graphs Energy Stored Q=VC implies that graphs of Q against V must be straight line graphs The gradient here is C Q W =1/2 QV V

Energy Stored The gradient here is 1/C V W =1/2 QV Q

We know we have The constant current means that we can work out the charge delivered from Q=It = 10 x 10-6 x 20 = 200 x 10-6C Now apply