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iB = 18 mA R 1 R x = R2 R3
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vo (full scale) = 626 mV; k = 0125 mV/N vR1 = ia R1 ; vR2 = (ia ib )R2 ; vR3 = ib R3 ; vR4 = ib R4 va vb vb vd vb vc vc vd i1 = ; i2 = ; i3 = ; i4 = R1 R2 R3 R4
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Section 1: Charge and Kirchhoff s Laws; Voltages and Currents 21 An isolated free electron is traveling through an
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electric eld from some initial point where its Coulombic potential energy per unit charge (voltage) is 17 kJ/C and velocity = 93 Mm/s to some nal point where its Coulombic potential energy per unit charge is 6 kJ/C Determine the change in velocity of the electron Neglect gravitational forces
25 The current in a semiconductor device results from
the motion of two different kinds of charge carriers: electrons and holes The holes and electrons have charge of equal magnitude but opposite sign In a particular device, suppose the electron density is 2 1019 electrons/m3 , and the hole density is 5 1018 holes/m3 This device has a cross-sectional area of 50 nm2 If the electrons are moving to the left at a velocity of 05 mm/s, and the holes are moving to the right at a velocity of 02 mm/s, what are: a The direction of the current in the semiconductor b The magnitude of the current in the device
22 The unit used for voltage is the volt, for current the
ampere, and for resistance the ohm Using the de nitions of voltage, current, and resistance, express each quantity in fundamental MKS units
26 The charge cycle shown in Figure P26 is an example
of a two-rate charge The current is held constant at 50 mA for 5 h Then it is switched to 20 mA for the next 5 h Find: a The total charge transferred to the battery b The energy transferred to the battery Hint: Recall that energy, w, is the integral of power, or P = dw/dt
23 Suppose the current owing through a wire is given
by the curve shown in Figure P23
4 i(t) (mA) 2 0 1 2 3 4 5 6 7 8 9 10 t (s)
2 4
175 V Battery voltage 15 V 125 V 1V
Figure P23
a Find the amount of charge, q, that ows through the wire between t1 = 0 and t2 = 1 s b Repeat part a for t2 = 2, 3, 4, 5, 6, 7, 8, 9, and 10 s c Sketch q(t) for 0 t 10 s
5 hrs
10 hrs
24 The capacity of a car battery is usually speci ed in
ampere-hours A battery rated at, say, 100 A-h should be able to supply 100 A for 1 hour, 50 A for 2 hours, 25 A for 4 hours, 1 A for 100 hours, or any other combination yielding a product of 100 A-h a How many coulombs of charge should we be able to draw from a fully charged 100 A-h battery b How many electrons does your answer to part a require
Battery current 50 mA 20 mA
5 hrs
10 hrs
Figure P26
2
Fundamentals of Electric Circuits
27 Batteries (eg, lead-acid batteries) store chemical
energy and convert it to electrical energy on demand Batteries do not store electrical charge or charge carriers Charge carriers (electrons) enter one terminal of the battery, acquire electrical potential energy and exit from the other terminal at a lower voltage Remember the electron has a negative charge! It is convenient to think of positive carriers owing in the opposite direction, ie, conventional current, and exiting at a higher voltage All currents in this course, unless otherwise stated, will be conventional current (Benjamin Franklin caused this mess!) For a battery with a rated voltage = 12 V and a rated capacity = 350 ampere-hours (A-h), determine: a The rated chemical energy stored in the battery b The total charge that can be supplied at the rated voltage
a The power is dissipates as heat or other losses b The energy dissipated by the heater in a 24-hour period c The cost of the energy if the power company charges at the rate 6 cents/kW-h
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