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Energy and power in electric circuits Va + + Vb - I Circuit element such as resistor, battery, … For qVab>0 : charge q looses potential energy., electric force does work on the charge Since current is stationary Charge is not gaining kinetic energy but energy qVab is transferred into circuit element, e.g., in the form of heat, light, … For qVab<0 : charge q gains potential energy, circuit element is a source of emf such as a battery If I is the current flowing through the element dQ I dt charge passing through the element in dt Potential energy of dQ changes by VabdQ Vab I dt Change of energy per time is the electric power, e.g., consumed by the circuit element dQ Vab dt Unit: 1VA=1JA/As=1J/s=1W P VI If circuit element is a resistor we obtain 2 V P VI RI 2 R Power delivered to a resistor If circuit element is a source (of emf) Rate a which source delivers power P VI E Ir I E I I 2 r Power dissipated by internal resistance of source Rate at which work is done on charge by nonelectrostatic (e.g., chemical) force An example: What is the rate at which the battery converts chemical into electrical energy? chemical to electrical Pconversion E I 12V 2 A 24W What is the power dissipated by the internal resistance of the battery? int ernal r of battery Pdissipated I 2r 4 A2 2 8W What is the power dissipated by the external resistor R? external R Pdissipated I 2 R 4 A2 4 16W Energy conservation chemical to electrical conversion P (per time): P int ernal r of battery dissipated +P external R dissipated EI I r I R 24W 8W 16W 2 2