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Chapter 1 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 1 Objectives • Understand and be able to use SI units and the standard prefixes for powers of 10. • Know and be able to use the definitions of voltage and current. • Know and be able to use the definitions of power and energy. • Be able to use the passive sign convention to calculate the power for an ideal basic circuit element given its voltage and current characteristics. Engr228 Chapter 1, Nilsson 9E 1 Engineering Problem Solving • All engineers share a considerable amount of common ground, particularly when it comes to problem solving. • Circuit analysis has long been a traditional introduction to the art of problem solving from an engineering perspective. The International System of Units (SI) Engr228 Chapter 1, Nilsson 9E 2 Derived Units in SI Standardized Prefixes to Signify Powers of 10 Engr228 Chapter 1, Nilsson 9E 3 Dimensional Analysis Dimensional analysis can be used to aid the solution to a problem by ensuring that the final units are correct • Examples – Find the number of seconds in a year – Find the number of miles in a light year (the speed of light is 186,287.5 miles per second) 31,557,600 seconds/year 5,878,786,100,000 miles Simple DC Circuit Current • Voltage • Current • Resistance Engr228 Chapter 1, Nilsson 9E 4 Charge • The symbol for charge is Q or q and the unit is coulomb (C). • Charge is bipolar, meaning that electrical effects are described in terms of positive and negative charges. • Electric charge exists in discrete quantities, which are integral multiples of the electronic charge ±1.6022×10-19 C. • Electrical effects are attributed to both the separation of charge, voltage, and charges in motion, current. In other words, voltage is potential energy while current is kinetic energy. Current and Charge Current is the rate of charge flow: I = dq/dt 1 ampere = 1 coulomb/second Engr228 Chapter 1, Nilsson 9E 5 Current and Charge • Current (designated by I or i) is the rate of flow of charge. • Current must be designated with both a direction and a magnitude. • These two currents are the same: Current and Charge: I = dq/dt Engr228 Chapter 1, Nilsson 9E 6 Types of Current Voltage (V or v) • Voltage is the measure of work required to move charge thru a circuit element. • The unit of voltage is volt (V) = Joule/Coulomb = J/C • Unlike current, voltage can exist between a pair of terminals whether a current is flowing or not, i.e., a battery Engr228 Chapter 1, Nilsson 9E 7 Circuit Elements • A circuit element most often has two terminals (sometimes three or more). • The relationship between the voltage v across the terminals and the current i through the device defines the circuit element model. Passive Sign Convention • Voltage and current can be either positive or negative, depending on how you specify a reference. To be consistent, we will adopt the Passive Sign Convention: Whenever the reference direction for the current in an element is in the direction of the reference voltage drop across the element, use a positive sign in any expression that relates the voltage to the current. Otherwise, use a negative sign. Engr228 Chapter 1, Nilsson 9E 8 Interpretation of Reference Directions Example of Voltage Polarities • Voltage (V or v) across an element requires both a magnitude and a polarity. • Example: (a)=(b), (c)=(d) Engr228 Chapter 1, Nilsson 9E 9 Power and Energy • Power is the time rate of expending or absorbing energy P = dw/dt where p = the power in watts, w = the energy in joules t = the time in seconds • From the definitions for current and voltage, power is also P = VI Power and the Passive Sign Convention • Since voltage and current can be either positive or negative, we use the passive sign convention to ensure that the sign of power is correct. • Power is positive if the reference direction for the current is in the direction of the reference drop across the terminals of an element. • When power is positive, the element is absorbing power. • When power is negative, the element is supplying power. Engr228 Chapter 1, Nilsson 9E 10 Example: Power How much power is absorbed by the three elements above? Pa = + 6 W, Pb = +6 W, Pc = -20 W (Note: (c) is actually supplying power) Textbook Problem 2.20 Hayt 7E • Determine which of the five sources are being charged (absorbing positive power), and show that the algebraic sum of the five absorbed power values is zero. Source 2 V source 8 V source -4 A source 10 V source -3 A source Absorbed Power (2 V)(-2 A) (8 V)(-2 A) (10 V)[-(-4 A)] (10 V)(-5 A) (10 V)[-(-3 A)] -4W - 16 W 40 W - 50 W 30 W Engr228 Chapter 1, Nilsson 9E 11 Chapter 1 Summary • • • • Defined SI units and the standard prefixes for powers of 10. Defined voltage and current. Defined power and energy. Explained the passive sign convention and used it to calculate the power for an ideal basic circuit element given its voltage and current. Engr228 Chapter 1, Nilsson 9E 12