Lesson 4: Series Circuits and Kirchhoff’s Voltage Law. Learning Objectives. Identify elements that are connected in series. State and apply KVL in analysis of a series circuit. Determine the net effect of series-aiding and series-opposing voltage sources.
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Learning Objectives • Identify elements that are connected in series. • State and apply KVL in analysis of a series circuit. • Determine the net effect of series-aiding and series-opposing voltage sources. • Compute the power dissipated by each element and the total power in a series circuit. • Describe the basic function of a fuse or a switch. • Draw a schematic of a typical electrical circuit, and explain the purpose of each component and indicate the polarity and current direction.
INTRODUCTION • Two types of current are readily available to the consumer today. • One is direct current (dc), in which ideally the flow of charge (current) does not change in magnitude (or direction) with time. • The other is sinusoidal alternating current (ac), in which the flow of charge is continually changing in magnitude (and direction) with time.
FIG. 5.4 Series connection of resistors. SERIES RESISTORS • Before the series connection is described, first recognize that every fixed resistor has only two terminals to connect in a configuration—it is therefore referred to as a two-terminal device.
FIG. 5.6 Series connection of resistors. FIG. 5.7 Series connection of four resistors of the same value SERIES RESISTORS
Series Circuits Two elements in a series Connected at a single point (node) No other current-carrying connections at this node A series circuitis constructed by connecting various elements in series
Series Circuits Normally Current will leave the positive terminal of a voltage source and move through the resistors Return to negative terminal of the source Current is the same everywhere in a series circuit
Series Circuits Current is similar to water flowing through a pipe Current leaving the element must be the same as the current entering the element Current = water flow rate Pressure = potential difference = voltage Same current passes through every element of a series circuit
Kirchhoff’s voltage law (1) Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero. Mathematically, KVL implies ET - V1 - V2 - V3 - ∙∙∙ - Vn = 0
Kirchhoff’s voltage law (2) Another way of stating KVL is: Summation of voltage rises is equal to the summation of voltage drops around a closed loop V1 + V2 + V3 + ∙∙∙ + Vn = ET being ET= E1+E2+E3+…+En
Kirchhoff’s Voltage Law (KVL) (3) A closed loop is any path that: Originates at a point Travels around a circuit Returns to the original point without retracing any segments
Kirchhoff’s Voltage Law (4) Summation of voltage rises is equal to the summation of voltage drops around a closed loop E1 + E2 = v1 + v2 + v3
Example Problem 1 Determine the unknown voltages in the network below:
Example Problem 2 Use Kirchhoff’s Voltage Law to determine the magnitude and polarity of the unknown voltage ES in the circuit below:
Resistors in Series Most complicated circuits can be simplified For a series circuit V1 + V2 + V3 = E IR1 + IR2 + IR3 = E I(R1 + R2 + R3 )= E I(R1 + R2 + R3 )= IRtotal (Note: I’s cancel)
Two resistors in series Two resistors in series can be replaced by an equivalent resistance Req.
Nresistors in series The equivalent resistance Req of any number of resistors in series is the sum of the individual resistances.
Example Problem 3 For the circuit below (with Rtot =800Ω), determine: • Direction and magnitude of current • Voltage drop across each resistor • Value of the unknown resistance
Power in a Series Circuit • Power dissipated by each resistor is determined by the power formulas: P = VI = V2/R = I2R
Power in a Series Circuit • Since energy must be conserved, power delivered by voltage source is equal to total power dissipated by resistors PT = P1 + P2 + P3 + ∙∙∙ + Pn
Example Problem 4 For the circuit below, determine: • Power dissipated by each resistor and total power dissipated by the circuit. • Verify that the summation of the power dissipated by each resistor equals the total power delivered by the voltage source.
Voltage Sources in Series • In a circuit with more than one source in series • Sources can be replaced by a single source having a value that is the sum or difference of the individual sources • Polarities must be taken into account
Voltage Sources in Series • Resultant source • Sum of the rises in one direction minus the sum of the voltages in the opposite direction
Interchanging Series Components • Order of series components • May be changed without affecting operation of circuit • Sources may be interchanged, but their polarities can not be reversed • After circuits have been redrawn, it may become easier to visualize circuit operation
Example Problem 5 Redraw the circuit below, showing a single voltage source and single resistor. Solve for the current in the circuit.
Switches The most basic circuit components is a switch. The switch below is known as a single-pole, single-throw (SPST) switch.
Fuses A fuse is a device that prevents excessive current to protect against overloads or possible fires. A fuse literally “blown” can not be reset.
Circuit breakers A circuit breaker also prevents excessive current in circuits however is uses an electro-mechanical mechanism that opens a switch. A “popped” circuit break can be reset.
Consolidated Schematic Circuit Breaker Ammeter Lamp Battery Fuse Voltmeter