ECE-320 CH02.pdf - Unix.eng.ua.edu

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G. Rizzoni, Principles and Applications of Electrical Engineering Problem solutions, Chapter 2Find:a) The charge transferred to the batteryb) The energy transferred to the battery.Analysis:a) To find the charge delivered to the battery during the charge cycle, we examine the charge-currentrelationship:thus:i =dqdttor1Q = i () t dtt05hrsdq = i ⋅ dt10hrsQ = 50mAdt + 20mAdt018000s5hrs36000s= 005 . dt + 002 . dt018000= 900 + 360= 1260Cb) To find the energy transferred to the battery, we examine the energy relationshipdwp = or dw = p(t)dtdtt1w = p(t)dt =t0tt10v(t)i(t)dtobserving that the energy delivered to the battery is the integral of the power over the charge cycle. Thus,180000= (0.05t +0.7536000t2)180000360000.75tw = 0.05(1+ ) dt +18000180000.02(1++ (0.02t +0.25360000.25t) dt18000t2)3600018000w =1732.5 J________________________________________________________________________Solution:Problem 2.5Known q<strong>ua</strong>ntities:Rated voltage of the battery; rated capacity of the battery.Find:a) The rated chemical energy stored in the batteryb) The total charge that can be supplied at the rated voltage.2.4
G. Rizzoni, Principles and Applications of Electrical Engineering Problem solutions, Chapter 2Analysis:a)∆PEc∆Q∆ V ≡ I =∆Q∆tChemical energy = ∆PE= ∆V⋅ ∆Q= ∆V⋅( I ⋅ ∆t)= 12 V 350 a hr 3600= 15.12 MJ.cshrAs the battery discharges, the voltage will decrease below the rated voltage. The remaining chemicalenergy stored in the battery is less useful or not useful.b) ∆ Q is the total charge passing through the battery and gaining 12 J/C of electrical energy.∆Q= I ⋅ ∆t= 350 a hr = 350= 1.26 MC.Cshr ⋅ 3600________________________________________________________________________Solution:Problem 2.6shrKnown q<strong>ua</strong>ntities:Resistance of external circuit.Find:a) Current supplied by an ideal voltage sourceb) Voltage supplied by an ideal current source.Assumptions:Ideal voltage and current sources.Analysis:a) An ideal voltage source produces a constant voltage at or below its rated current. Current is determinedby the power required by the external circuit (modeled as R).VsI =RP = Vs⋅ Ib) An ideal current source produces a constant current at or below its rated voltage. Voltage is determinedby the power demanded by the external circuit (modeled as R).V = I⋅ RP = V ⋅sI sA real source will overheat and, perhaps, burn up if its rated power is exceeded.________________________________________________________________________2.5
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