Introduction to EE 207: Foundations of Chapter 1 Basic Concepts Electrical Engineering 1.2 Systems of Units • One millivolt is one millionth of a volt: (a) True (b) False ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • The prefix micro stands for: (a) 106 (b) 103 (c) 10−3 (d) 10−6 ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • The voltage 2,000,000 V can be expressed in powers of 10 as: (a) 2 mV (b) 2 kV (c) 2 MV (d) 2 GV ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • Example: convert 17.158 kg to milligrams. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • Example: convert 0.0013 A to nanoamperes. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • Example: convert 56 µC to kC. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… 1.3 Charge and Current The charge (e) of an electron is negative and equal in magnitude to 1.602×10−19 C, while a proton carries a positive charge of the same magnitude. Mathematically, the relationship between current i, charge q, and time t is 1 ampere = 1 coulomb/second ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… A direct current (dc) flows only in one direction and can be constant or time varying. We will use the symbol ( I ) to represent a constant current. (dc) An alternating current (ac) is a current that changes direction with respect to time. If the current varies with respect to time we will use the symbol (i). (ac) A negative current of −5 A flowing in one direction as shown is the same as a current of +5 A flowing in the opposite direction. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Example 1.1: How much charge is represented by 4600 electrons? ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Example: Determine the current flowing through an element if the charge flow is given by q(t) = (8t2 + 4t – 2) C ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Example 1.2: The total charge entering a terminal is given by q = 5t sin(4πt) mC Calculate the current at t = 0.5 s. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Practice Problem 1.2: The total charge entering a terminal is given by q = (10 − 10e−2t) mC find the current at t = 1.0 s. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Example 1.3: Determine the total charge entering a terminal between t = 1 s and t = 2 s if the current passing the terminal is i = (3t2 − t) A ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Practice Problem 1.3: The current flowing through an element is Calculate the charge entering the element from t = 0 to t = 2 s ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Example: The charge flowing in a wire is shown. Sketch the corresponding current. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Problem 1.8: The current flowing in a device is shown. Calculate the total charge through the device. ………………………………………………………………………………………………… 1.4 Voltage To move the electron in a conductor we need work, or an energy transfer. This is done by an external electromotive force (emf), typically by a battery. This emf is also known as voltage or potential difference. Voltage is the energy required to move a unit charge from a reference point (−) to another point (+), measured in volts (V). w is energy in joules (J) and q is charge in coulombs (C). 1 volt = 1 joule/coulomb = 1 newton-meter/coulomb. The plus (+) and minus (−) signs are used to define reference direction or voltage polarity ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… vab can be interpreted as: the potential at point a with respect to point b is vab point a is at a potential of vab volts higher than point b Point b is at a potential of -vab volts higher than point a We can also say that vab = -vba A constant voltage is called a dc voltage and is represented by V. A sinusoidally time-varying voltage is called an ac voltage and is represented by v. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • 1.5 Power and Energy Power is the time rate of expending or absorbing energy, measured in watts (W). Electric power example: a 10-watt LED bulb gives more light than a 6-watt bulb. Electricity bills are based on how much electric energy is used over one month. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… We write this relationship as p is power in watts (W), w is energy in joules (J), and t is time in seconds (s). This power is a time-varying quantity and is called instantaneous power. If the power has a: Positive (+) sign → power is delivered to or absorbed by the element. Negative (-) sign → power is supplied or generated by the element. Passive sign convention: when current enters through the positive terminal of an element → p = +vi when current enters through the negative terminal of an element → p = −vi An absorbing power of −12 W is equivalent to a supplying power of +12 W. In general: Positive (+) power absorbed = Negative (−) power supplied. • The law of conservation of energy requires that the algebraic sum of power in a circuit at any time must be zero. • Energy is the capacity to do work, measured in joules (J). • The energy absorbed or supplied by an element from time t0 to time t is • Example 1.4: An energy source forces a constant current of 2 A for 10 s to flow through an LED bulb. If 2.3 kJ is given off in the form of light and heat energy, calculate the voltage drop across the bulb. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • Example 1.5: Find the power delivered to an element at t = 3 ms if the current entering its positive terminal is i = 5 cos(60π t) A and the voltage is: • (a) v = 3i ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • Example 1.5: Find the power delivered to an element at t = 3 ms if the current entering its positive terminal is i = 5 cos(60π t) A and the voltage is: • (b) v = 3 di∕dt ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… 9 • Example 1.6: How much energy does a 10-W LED bulb consume in two hours? ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… • Circuit analysis determines voltages across (or currents through) the elements of the circuit. • An active element can generate energy while a passive element cannot. • Important active elements include voltage or current sources. • There are two kinds of sources: independent and dependent sources. • An independent source provides a voltage or current that is independent of other voltages or currents. • A dependent source provides a voltage or current that is dependent (controlled) by another voltage or current. There are four possible types of dependent sources: voltage-dependent voltage source current-dependent voltage source voltage-dependent current source current-dependent current source 10 • 1.6 Circuit Elements • A current-dependent voltage source is a voltage source with a value that depends on a current. Similarly, a voltage-dependent current source is a current source with a value that depends on a voltage. Example: In the circuit shown, the 5 V source is a constant (dc) source, and the current-dependent voltage source has the value of 10i V (and not 10i A) because it is a voltage source. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… 11 Example 1.7: Calculate the power supplied or absorbed by each element, and verify if the law of conservation of energy applies. • Example 1.7 (continued): • Practice Problem 1.7: Compute the power absorbed or supplied by each component of the circuit, and verify if the law of conservation of energy applies. ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 12
