8 Series Circuits UEENEEE104A DC CIRCUITS PURPOSE: This section introduces the series circuit and the basic laws applicable to series circuits. 8 TO ACHIEVE THE PURPOSE OF THIS SECTION: At the end of this section the student will be able to: Define what is meant by the term series circuit and draw circuit diagrams of series connected components. State the basic laws related to current, voltage, power and equivalent resistance for series connected resistive circuits. Simplify a series circuit to one containing a single equivalent resistance.

Calculate circuit current, applied voltage, equivalent resistance and total power dissipation for a series circuit. Calculate the voltage drop, current and power dissipation for each resistor in a series circuit. List the affects of an open circuit and a short circuit on the current flowing in a series circuit. L

Electrical Principles BY PETER PHILLIPS Page 109 - 124 REFERENCES: Electrical Principles BY PETER PHILLIPS L

1.WHAT IS A SERIES CIRCUIT? Series circuit - a circuit in which all components are connected so as to allow only one path for current to flow. Switch and Lamp in series Lamps in series Figure 1 L

+ - 2.CURRENT FLOW IN A SERIES CIRCUIT A series circuit has only one current path, therefore there is only ______________________. one current R1 + IT I1 R2 I2 R3 - I3 Figure 2 Therefore, the basic rule relating to current in a series circuit states - same The current in a series circuit is the _________________ in all parts of the circuit. L

Based on the arrangement shown in figure 2, the current in various parts of a series circuit may be expressed mathematically as - IT = I1 = I2 = I3 where: IT = supply current I1 = current through resistor R1 I2 = current through resistor R2 I3 = current through resistor R3 L

+ - 3. RESISTANCE OF A SERIES CIRCUIT Consider three resistors connected in series. R1 + R2 - R3 Figure 3 As current flows through the circuit it passes through each resistor in turn. That is, the total resistance seen by the power supply will be the combination of all resistances. Therefore, the basic rule relating to resistance in a series circuit states - sum The equivalent or total resistance is equal to the __________ of the individual resistances. L

RT = R1 + R2 + R3 RT = R1 + R2 + R3 = 5 + 4 + 11 = 20 Ω This statement may be expressed mathematically as - RT = R1 + R2 + R3 where: RT = total circuit resistance R1 = resistance of resistor R1 R2 = resistance of resistor R2 R3 = resistance of resistor R3 Example: 1 Three resistors having resistances of 5Ω, 4Ω and 11Ω are connected in series. Calculate the total resistance of the circuit. RT = R1 + R2 + R3 = 5 + 4 + 11 = 20 Ω L

Example: 2 Determine the resistance of the resistor R2 in the circuit of figure 4. R1 + 35 Ω R2 RT = 75 Ω 22 Ω - R3 RT = R1 + R2 + R3 R2 = RT - R1 – R3 Figure 4 R2 = RT - R1 - R3 = 75 - 35 - 22 = 18 Ω L

R = V I = V I V = I R R 4. OHM'S LAW AND THE SERIES CIRCUIT As seen previously, values of voltage, current and resistance may be determined by the application of Ohm's law. The three equations associated with Ohm's law are - I = V R R = V I V = I R As is the case with the basic electric circuit, Ohm's law may be applied to a series circuit to determine values of voltage, current and resistance. Ohm's law may be applied to – an entire series circuit - using total circuit values, for example, any individual section of a series circuit - using section values, for example, L

+ RT = R1 + R2 + R3 = 50 + 20 + 30 = 100 Ω - I = V = 200 = 2 A R 100 + Example: 3 For the circuit of figure 5, determine - (a) total circuit resistance (b) circuit current R1 + 50 Ω R2 VT = 200 V 20 Ω RT = R1 + R2 + R3 = 50 + 20 + 30 = 100 Ω 30 Ω - R3 I = V = 200 = 2 A R 100 Figure 5 Example: 4 Determine the voltage across resistor R2 in the circuit of figure 6. R1 + IT = 1.5 A V = I R2 V = I R2 = 1.5 x 40 = 60 V 40 Ω R2 - R3 Figure 6 L

+ - 5. VOLTAGES IN A SERIES CIRCUIT V1 Consider the circuit shown in figure 7. V1 R1 + IT = 1 A 10 Ω 6 Ω V2 VT R2 4 Ω - R3 V3 Figure 7 Assuming the current flowing in the circuit and the value of the individual resistances are known,the voltages across each resistor may be determined. These voltages are known as the circuit ________________________________________. The circuit voltage drops may be determined by applying Ohm's law to each resistor individually. voltage drops L

The voltage drop across the resistor R1 is determined by applying Ohm's law using only values associated with R1 - V1 = I R1 = 1 x 10 = 10 V The voltage drop across the resistor R2 is determined by applying Ohm's law using only values associated with R2 - V2 = I R2 = 1 x 6 = 6 V The voltage drop across R3 is determined in the same way, but using only values associated with R3 - V3 = I R3 = 1 x 4 = 4 V If each of the individual voltage drops are known, the applied voltage may be determined. The rule for voltages in a series circuit, known as Kirchhoff's voltage law, is - The applied voltage is equal to the _________________ of the individual voltage drops.. sum L

VT = V1 + V2 + V3 This statement may be expressed mathematically as - where: VT = the applied voltage V1 = the voltage drop across resistor R1 V2 = the voltage drop across resistor R2 V3 = the voltage drop across resistor R3 L

For the series circuit shown in figure 8, determine - Example: 5 For the series circuit shown in figure 8, determine - (a) total circuit resistance (b) the voltage drop across each resistor (c) the supply voltage. R1 (a) RT = R1 + R2 + R3 = 5.6 + 10 + 18 = 33.6 Ω IT = 0.6 A 5.6Ω VT 10Ω R2 18 Ω (b) V1 = I R1 = 0.6 x 5.6 = 3.36V R3 V2 = I R2 = 0.6 x 10= 6 V V3 = I R3 = 0.6 x 18 = 10.8V Figure 8 VT = V1 + V2 + V3 =3.38 + 6 + 10.8 = 20.16 V (c) L

Example: 6 Determine the voltage drop across the resistor R3 in the circuit of figure 9. R1 16 V VT = V1 + V2 + V3 V3 = VT - V1 – V2 VT = 32 V 7 V R2 R3 V3 = VT - V1 – V2 = 32 – 16 - 7 = 9 V Figure 9 L

+ - 6. VOLTAGE DIVIDER CIRCUIT The voltage drop across a particular resistor in a series circuit may be determined using the voltage divider. The advantage of the voltage divider is that voltage drops may be determined without knowing the circuit current. The basic arrangement for the voltage divider is shown in figure 10. + R1 VT R2 V2 - Figure 10 Example: 7 For the circuit of figure 10, assume the supply voltage is 10V, R1 has a value of 1kΩ and R2 a value of 3kΩ. Determine the voltage drop across the resistor R2. L

PT = P1 + P2 + P3 7. POWER IN A SERIES CIRCUIT Each component in a series circuit dissipates power and the total power delivered to a circuit is supplied by the circuit power supply. Therefore, it can be stated - sum The total power supplied to a series circuit is equal to the ____________ of the powers dissipated by each component. Writing this statement in the form of an equation gives - PT = P1 + P2 + P3 where: PT = total power dissipated P1 = power dissipated by component 1 P2 = power dissipated by component 2 P3 = power dissipated by component 3 L

+ - Example: 8 For the circuit shown in figure 11, calculate the - (a) circuit current (b) total circuit resistance (c) voltage drop across R1 (d) applied voltage (e) power dissipated by each resistor (f) total power dissipated + R1 150Ω VT R2 50 V 100 Ω - Figure 11 I = V2 R2 = 50 100 = 0.5A (a) (d) VT = V1 + V2 =75 + 50 = 125 V (e) (f) PT = P1 + P2 =37.5 + 25 = 62.5 W P1 = V1 x I =75 x 0.5 = 37.5W (b) RT = R1 + R2 = 150 + 100 = 250 Ω P2 = V2 x I =50 x 0.5 = 25W (c) V1 = I x R1 =0.5 x 150 = 75 V L

+ + - - 8. EFFECT OF AN OPEN CIRCUIT IN A SERIES CIRCUIT Consider three lamps connected in series, as shown in figure 12. What would be the effect on the circuit of say lamp 2 going open circuit? Lamp 1 Lamp 1 + - + - Open circuit Lamp 2 Lamp 3 Lamp 3 Figure 13 Figure 14 The open circuit would cause the circuit current to _____________________________. Drop to zero L

The effects of an open circuit in any part of a series circuit are – circuit current is ________________ the resistance of the circuit is ________________ the voltage across the open circuit equals the _____________________ the voltage across all other components equals _________________ all components in the circuit _______________ working. zero infinite supply volts zero stop 9. EFFECT OF A SHORT CIRCUIT IN A SERIES CIRCUIT Consider three lamps connected in series, as shown in figure 14. What would be the effect on the circuit of say lamp 3 going short circuit? L

+ + - - Lamp 1 Lamp 1 Short circuit Lamp 2 Lamp 2 Lamp 3 Lamp 3 Figure 14 Figure 15 The short circuit would cause the circuit current to _____________________________. increase The effects of a short circuit in any part of a series circuit are – circuit current is ________________ the resistance of the circuit is ________________ the voltage across the short circuit equals _____________________ the voltage across all other components _________________ all components in the rest of the circuit work _______________ because of the increased voltage drop across them. increased decreased Zero volts increases harder L

Equations lesson 7 Series Circuit IT = I1 = I2 = I3 RT = R1 + R2 + R3 VT = V1 + V2 + V3 L

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