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1 SERIES CIRCUITS Benchmark Companies Inc PO Box 473768 Aurora CO 80047

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2 Series Circuit A series circuit is defined as having all components connected in series (head to toe) with each other

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3 Voltage, Current, and Resistance in Series Circuits In this section we will discuss the properties of Ohms Laws and the relationship between each. Current (I) Amps Voltage (V) Volts Resistance (Ω) Ohms V=IR

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4 Voltage, Current, and Resistance in Series Circuits The total current in a series circuit is equal to the current in any other part of the circuit. I 1 = current in the first part I 2 = current in the second part I 3 = current in the third part, etc. Formula: I T = I1 I1 = I2 I2 = I 3 = etc. Total Current in a Series Circuit

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5 Voltage, Current, and Resistance in Series Circuits The total current in a series circuit is equal to the current in any other part of the circuit. Total Current in a Series Circuit Therefore I T =I R1 =I R2 =I R3 = etc.

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6 where V T = total voltage V 1 = voltage across first part V 2 = voltage across second part V 3 = voltage across third part, etc. The total voltage in a series circuit is equal to the sum of the voltage drops across all the parts of the circuit. Formula: VT VT = V 1 + V 2 + V 3 + etc. Total Voltage in a Series Circuit

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7 The total voltage in a series circuit is equal to the sum of the voltage drops across all the parts of the circuit. Therefore: VT VT = V R1 + V R2 + V R3. Total Voltage in a Series Circuit

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8 The total voltage in a series circuit is equal to the sum of the voltage drops across all the parts of the circuit. Therefore: V T = 10V + 10V + 20V= 40V. Total Voltage in a Series Circuit

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9 where R T = total resistance R 1 = resistance of first part R 2 = resistance of second part R 3 = resistance of third part, etc. The total resistance of a series circuit is equal to the sum of the resistances of all the parts of the circuit. Formula: RT RT = R 1 + R2 R2 + R 3 + etc. Total Resistance in a Series Circuit

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10 The total resistance of a series circuit is equal to the sum of the resistances of all the parts of the circuit. Therefore: RT RT = 10Ω + + 20Ω = 40Ω Total Resistance in a Series Circuit

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11 Series Equivalent Circuit

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12 Example 4-1 A 6-V 20- filament and a 12-V 40- filament are connected in series with a 20- limiting resistor dropping 6 V across it and 0.3 A through it. Find: (a) the total voltage (b) the total current (c) the total resistance Continued

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13 (c) Find the total resistance. 1. Write the formula. R T = R 1 + R 2 + R 3 2. Substitute numbers. R T = 20 + 40 + 20 = 80 Solution: using the equations derived previously (a) Find the total voltage. 1. Write the formula. V T = V 1 + V 2 + V 3 2. Substitute numbers. V T = 6 + 12 + 6 = 24 V (b) Find the total current. 1. Write the formula. I T = I 1 = I 2 = I 3 2. Substitute numbers. I T = I 1 = =I 2 =I 3 = 0.3 A

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14 Using Ohm’s Law in Series Circuits Ohm’s law may be used for the individual parts of a series circuit. When it is used on a particular part of a circuit, great care must be taken to use only the voltage, current, and resistance of that particular part. This may be easily remembered by using the correct subscripts when writing the Ohm’s-law formula for a particular part. For the first part:V 1 = I 1 x R1R1 For the second part:V 2 = I 2 x R2R2 For the third part:V 3 = I 3 x R3R3

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15 Using Ohm’s Law for Total Values in Series Circuits A resistor, doorbell, and buzzer are connected in series across a voltage source. The resistor has a resistance R 1 of 45 , the doorbell resistance R 2 is 60 , and the buzzer resistance R 3 is 50 . I 3 is 0.2 A. Find the value of V T. Example Finding the Total Voltage Continued

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16 3. Find the total voltage. V T = I T x R T V T = 0.2 x 155 = 31 VAns. 1. Find the total current. I T = I 1 = I 2 = I 3 = 0.2 AAns. 2. Find the total resistance. R T = R 1 + R 2 + R 3 R T = 45 + 60 + 50 = 155 Ans. Solution

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17 Control of Current in a Series Circuit Example 4-27 1. Write the formula. V T = V X + V L 2. Substitute numbers. 24 = V X + 12 3. Transpose the 12. 24 - 12 = V X 4. Subtract. 12 = V X = 12 V What resistance must be added in series with a lamp rated at 12 V, 0.3 A order to operate it from a 24 V source? Solution

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18 Series Circuit Current is constant Why? Only one path for the current to take Kirchhoff’s Current Law Voltages through circuit equals zero Kirchhoff’s Voltage Law

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19 Introducing Kirchhoff’s Voltage Law Net Voltage for a circuit = 0 Sum of all voltage drops and voltage rises in a circuit (a closed loop) equals zero

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20 Example One 10Ω resistor connected to the 6V power source (batteries). Add another 10Ω resistor to the circuit in series to the first resistor. Q:What is the equivalent resistance, R? What will happen to the value of the current through each resistor? What will happen to the value of the voltage across each resistor?

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21 Example: What is happening in theory

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22 Example: T he actual data In reality, the data we get is not the same as what we get in theory. Why? Because when we calculate numbers in theory, we are dealing with an ideal system. In reality there are sources of error in every aspect, which make our numbers imperfect.

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23 1. Write the formulas for finding I T, V T, and R T, in series circuit. Exercise 2. A 5 V 17 and a 10 V 40 filaments are in series with a 17 limiting resistor using 6 V and 0.3 A. Find: (a) V T ; (b) I T ; and (c) R T. (21 V; 74 ; 0.3 A) I T = I 1 = I 2 = I 3 = etc. V T = V 1 + V 2 + V 3 + etc. R T = R 1 + R 2 + R 3 + etc.

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24 3. A resistance R 1 = 25 , a doorbell R 2 = 50 , and a buzzer R 3 =38 , are connected in series.The current through the buzzer is I 3 = 0.4 A. Find V T. Exercise 4. Three resistances are connected in series. V 1 = 12.6 V, I 1 = 1.1 A, R 1 = 11 , V 2 = 24 V, R 2 = 21 , V 3 = 48 V, R 3 = 42 . Find V T, I T, R T. (84.6 V, 1.14 A, 74 ) (45.2 V)

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25 End of Lesson

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Series & Parallel Circuits

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