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EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

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EGR 1301 Electrical Work Method 1 Work (or Energy) = Force x Distance Force = magnetic force on electrons Distance = traveled in wire or resistor V batt R I V drop = I R

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EGR 1301 Voltage – What Is It? Energy per unit charge of current 1 Volt = Or V = E/Q So E = VQ 1 Coulomb(charge) 1 Joule (energy)

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EGR 1301 Example 1: Battery A charge of Q = 50 C flows through a 12 V battery. a) How much energy is imparted to the charge? E = VQ = (12 V)(50 C) = 240 J b) Where does the energy come from? The electro-chemical reactions in the battery.

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EGR 1301 Electrical Work Method 2 Recall: Power = Energy/Time So, or Recall: Power = Voltage*Current (P =V I ) So, V batt R I V drop = I R t E P = E = Pt R V2V2 E = V I t = t = I 2 R t

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EGR 1301 Example 2: Water Heater How much energy does a hot water heater use if it draws 10 A from a 120 V wall outlet for 1 hour? I = 10 A, V = 120 V, t = 1 hr = 3600 s E = VIt = (120 V)(10 A)(3600 s) = 4.32 MJ Units check: V*A*s = J/C * C/s * s = J

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EGR 1301 Capacitors Energy is stored in electric field between the plates. Recall: From method 1: E = QV VC + - V Q C = Conductor Insulator Stored Charge or Q = VC

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EGR 1301 Capacitors From previous slide: E = QV and Q = VC Charge builds up on either side of capacitor Each bit of charge requires more energy V C V V V

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EGR 1301 Example 3: Capacitor A 50 μF capacitor is charged to 10 V. What energy is stored? C = 50 μF, V = 10 V E = ½CV 2 = ½(50 μF)(10 V) 2 = ½(50x10 -6 F)(10 V) 2 = 2.5x10 -3 J = 2.5 mJ

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EGR 1301 Example 3: Camera Flash Assume a light bulb and a camera flash give the same light per unit energy. The camera flash has a 100 μF capacitor, charged to 250 V. How many 60 W light bulbs is this energy usage equivalent to if the camera discharges in t = 0.01 s?

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EGR 1301 Example 3: Camera Flash How many 60W light bulbs is this energy usage equivalent to if the camera discharges in t = 0.01 s? C = 100 μF, V = 250 V, t = 0.01 s E = ½CV 2 = ½(100x10 -6 F)(250 V) 2 = J 1 bulb: E = Pt E bulbs = NPt = N(60 W)(0.01 s) = 0.6*N J 0.6*N J = J N = 3.125/0.6 = 5.21 bulbs

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EGR 1301 Inductor Energy is stored in magnetic field inside the coil. Similar to the capacitor, except using current instead of voltage L +-V I

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