1	Chapter 5 Series Circuits
2	Series Circuits Two elements in a series Connected at a single point No other current-carrying connections at this point A series circuit is constructed by connecting various elements in series
3	Series Circuits Normally Current will leave the positive terminal of a voltage source Move through the resistors Return to negative terminal of the source
4	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 Same current passes through every element of a series circuit
5	Series Circuits The laws, theorems, and rules that you apply to DC circuits Also apply to AC circuits
6	Kirchhoff’s Voltage Law (KVL) The algebraic sum of the voltage that rises and drops around a closed loop is equal to zero E_T - V₁ - V₂ - V₃ - ∙∙∙ - V_n= 0
7	Kirchhoff’s Voltage Law (KVL) 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 + ∙∙∙ + V_n = E_T
8	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 )= IR_total (Note: I’s cancel)
9	Resistors in Series Total resistance in a series circuit is the sum of all the resistor values
10	Power in a Series Circuit Power dissipated by each resistor is determined by the power formulas: P = VI = V²/R = I²R
11	Power in a Series Circuit Since energy must be conserved, power delivered by voltage source is equal to total power dissipated by resistors P_T = P₁ + P₂ + P₃ + ∙∙∙ + P_n
12	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
13	Voltage Sources in Series Resultant source Sum of the rises in one direction minus the sum of the voltages in the opposite direction
14	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
15	The Voltage Divider Rule Voltage applied to a series circuit Will be dropped across all the resistors in proportion to the magnitude of the individual resistors
16	The Voltage Divider Rule Voltage dropped across each resistor may be determined by the voltage across any other resistor (or combination of resistors) by using the voltage divider rule expressed as: The subscripts must match (x and y)
17	Voltage Divider Rule Application If a single resistor is very large compared to the other series resistors, the voltage across that resistor will be the source voltage If the resistor is very small, the voltage across it will be essentially zero
18	Voltage Divider Rule Application If a resistor is more than 100 times larger than another resistor Smaller resistor can be neglected
19	Circuit Ground Ground Point of reference or a common point in a circuit for making measurements One type of grounding is chassis ground In this type of grounding Common point of circuit is often the metal chassis of the piece of equipment
20	Circuit Ground Chassis ground Often connected to Earth Ground Earth ground Physically connected to the earth by a metal pipe or rod
21	Circuit Ground If a fault occurs within a circuit, the current is redirected to the earth Voltages are often measured with respect to ground
22	Double Subscripts For the circuit shown, we can express the voltage between any two node points (a and b) as V_ab. If a is at a higher potential than b, then V_ab is positive
23	Double Subscripts If b is at a higher potential than a, then V_ab is negative In this case, V_abwould be negative
24	Double Subscripts
25	Double Subscripts To determine correct polarity Calculate all voltage drops across all components Assign polarities As you go around a circuit, add the gains and subtract the drops
26	Double Subscripts Be sure to take the sign of the polarity on the same side of the source or element as you go around the circuit
27	Single Subscripts In a circuit with a ground reference point Voltages may be expressed with respect to that reference point V_a Voltage at point a with respect to ground Ground represents a point of zero reference potential
28	Single Subscripts Any voltage with a single subscript is with respect to ground This is the same as V_a(0)
29	Single Subscripts If voltages at various points in a circuit are known with respect to ground, then the voltage between points is easily determined V_ab = V_a – V_b
30	Point Sources Voltage source given with respect to ground May be represented by a voltage at a single point (node) in the circuit This voltage may be referred to as a point source
31	Point Sources Voltages at these points represent voltages with respect to ground, even if ground is not shown Point sources simplify representation of a circuit
32	Internal Resistance of Voltage Sources Ideal sources have no internal resistance In an ideal source Terminal voltage does not change when the load changes For a practical source There is internal resistance
33	Internal Resistance of Voltage Sources As the load changes Drop across the internal resistance changes Terminal voltage changes
34	Ammeter Loading Effects An ammeter is placed in a circuit to make a measurement Resistance will affect the circuit Amount of loading is dependent upon the instrument and the circuit
35	Ammeter Loading Effects If resistance of the meter is small compared to the resistance of the circuit, the loading effect will be small