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Lesson 19 Electric Circuits Eleanor Roosevelt High School Chin-Sung Lin Electric Circuits • Any path along which electrons can flow is a circuit • Complete circuit with no gaps • A gap/break in electric circuit results in a complete stop in the flow of electricity Electric Circuits Electric Circuits Electric Circuits • The components are commonly connected in one of the two ways, series or parallel Series Circuits • When connected in series, they form a single pathway for current to flow Series Circuits • Draw the schematic diagram Series Circuits • Schematic diagram Parallel Circuits • When connected in parallel, they form branches • Each branch is a separate path for current Parallel Circuits • Draw the schematic diagram Parallel Circuits • Schematic diagram Series Circuits Series Circuits • Label the circuit Series Circuits • Label the circuit + V1 – R1 R2 + V2 – I1 I + V – I2 Series Circuits • Electric current has a single pathway, so the current passing through each electronic device is the same + V1 – R1 R2 + V2 – I1 I + V – I2 I = I1 = I2 Series Circuits • Water flow model of series circuits Series Circuits • The total voltage is the sum of individual voltage drops along the circuit path V = V 1 + V2 + V1 – R1 R2 + V2 – I1 I + V – I2 Series Circuits V = V1 + V2 V = IR (Ohm’s Law applied to each device) IReq = I1R1 + I2R2 since I = I1 = I2 Req = R1 + R2 Series Circuits • The total resistance is the sum of individual resistances along the circuit path Req = R1 + R2 + V1 – R1 R2 + V2 – I1 I + V – I2 Series Circuits • The current in the circuit is numerically equal to the voltages supplied by the source divided by the total resistance of the circuit (Ohm’s law) V = I Req = I (R1 + R2) I = V / Req =V / (R1 + R2) Series Circuits • What will happen to the resistance if the number of devices increases? Series Circuits • What will happen to the resistance if the number of devices increases? As the number of devices increases, the overall resistance of the circuit is increased Series Circuits • Why is the overall resistance of the circuit increased as the number of devices increases? R1 + V1 – R2 + V2 – I1 I2 I R3 + V + – V3 – I3 R4 + V4 – I4 Series Circuits • Why is the overall resistance of the circuit increased as the number of devices increases? Voltage drop for the device decreases, the total current is decreased, resistance is increased R1 + V1 – R2 + V2 – I1 I2 I R3 + V + – V3 – I3 R4 + V4 – I4 Series Circuits • The overall resistance of the circuit is higher than any resistance of the existing devices Series Circuits • The amount of power consumed by the entire circuit is equal to the sum of the power consumed by each device V = V1 + V2 and I = I1 = I2 IV = I1V1 + I2V2 since P = IV (applied to each device) P = P1 + P2 Series Circuits Series Circuits I = I1 = I2 V = V 1 + V2 Req = R1 + R2 P = P1 + P2 Series Circuits Exercise • Three 3-Ω resistors placed in series would provide a resistance which is equivalent to one _____Ω- resistor • Three resistors with resistance values of 2-Ω , 4-Ω , and 6-Ω are placed in series. These would provide a resistance which is equivalent to one _____Ω- resistor Series Circuits Exercise • As the number of resistors in a series circuit increases, the overall resistance __________ and the current in the circuit __________ • Three identical light bulbs are connected in series and connected to a battery. Compare the brightness of them Series Circuits Exercise • A circuit has one resistor and the current is 4 A. If we add another identical resistor into the circuit in series, the current will become _________ A • A circuit has one resistor and the current is 4 A. If we add another 3 identical resistors into the circuit in series, the current will become _________ A Series Circuits Exercise • Calculate the total resistance R and total current I 300 Ω 200 Ω 4.5 V I Series Circuits Exercise • Calculate the equivalent resistance and voltage V of the cell 40 Ω 80 Ω V 0.1 A Series Circuits Exercise • Calculate the resistance R 300 Ω R 3V 0.002 A Series Circuits Exercise • If the voltage drop for the 10 Ω resistor is 2 V, calculate the total current I and the voltage V of the cell 10 Ω 40 Ω + 2V – V I Series Circuits Exercise • Calculate and compare V1 and V2 10 Ω 40 Ω + V1 – + V2 – 10 V Series Circuits Exercise • Calculate the Power P1, P2, and total power P of the circuit 10 Ω 40 Ω P1 P2 10 V Series Circuits Exercise • Calculate all the unknown quantities in the diagram + V1 – 200 Ω + V2 – 400 Ω I1 I + 3V – I2 Series Circuits • What will happen to the circuit if we add a wire to the circuit? Series Circuits • What is the disadvantage of the series circuits? Series Circuits • What is the disadvantage of the series circuits? If one device fails, current in whole circuit ceases and none of the devices will work When more devices added, the total current reduced Parallel Circuits Parallel Circuits • Label the circuit Parallel Circuits • Label the circuit + V1 – I1 + V2 – I2 R1 R2 I + V – Parallel Circuits • Each device connected to the same two points of the circuit. The voltage is the same across each device + V1 – I1 + V2 – I2 R1 R2 I + V – V = V 1 = V2 Parallel Circuits • Water flow model of parallel circuits Parallel Circuits • The total current in the circuit equals the sum of currents in its parallel branches + V1 – I1 + V2 – I2 R1 R2 I + V – I = I1 + I2 Parallel Circuits I = I1 + I2 I = V/R (Ohm’s Law applied to each device) V/Req = V1 / R1 + V2 / R2 Since V = V1 = V2 1 /Req = 1 / R1 + 1 / R2 Req = R1 R2 / (R1 + R2 ) or Parallel Circuits • The reciprocal of total resistance is the sum of reciprocals of individual resistances in the circuit + V1 – R1 R2 I + V2 – + V – 1 / Req = 1 / R1 + 1 / R2 I1 I2 Parallel Circuits • The current in the circuit is numerically equal to the voltages supplied by the source divided by the total resistance of the circuit (Ohm’s law) V = I Req = I R1 R2 / (R1 + R2) I = V / Req =V (R1 + R2) / R1 R2 Parallel Circuits • What will happen to the resistance if the number of parallel branches increases? Parallel Circuits • What will happen to the resistance if the number of parallel branches increases? As the number of parallel branches increase, the overall resistance of the circuit is decreased Parallel Circuits • Why is the overall resistance of the circuit decreased as the number of parallel branches increases? R1 R2 R3 R4 I + V1 – I1 + V2 – I2 + V3 – I3 + V4 – I4 + V – Parallel Circuits • Why is the overall resistance of the circuit decreased as the number of parallel branches increases? R1 R2 R3 R4 Total current is increased, resistance is decreased I + V1 – I1 + V2 – I2 + V3 – I3 + V4 – I4 + V – Parallel Circuits • The overall resistance of the circuit is lowered than any resistance of the added branches Parallel Circuits • The amount of power consumed by the entire circuit is equal to the sum of the power consumed by each device V = V1 = V2 and I = I1 + I2 IV = I1V1 + I2V2 since P = IV (applied to each device) P = P1 + P2 Parallel Circuits Parallel Circuits I = I1 + I2 V = V1 = V2 1/Req = 1/R1 + 1/R2 Req = R1 R2 / (R1 + R2 ) P = P1 + P2 or Parallel Circuits Exercise • Three 3-Ω resistors placed in parallel would provide a resistance which is equivalent to one _____Ω- resistor • Two resistors with resistance values of 20-Ω and 40-Ω are placed in parallel. These would provide a resistance which is equivalent to one _____Ω- resistor Parallel Circuits Exercise • As more and more resistors are added in parallel to a circuit, the equivalent resistance of the circuit ____________ and the total current of the circuit ____________ • Three identical light bulbs are connected in parallel and connected to a battery. Compare the brightness of them Parallel Circuits Exercise • A circuit has one resistor and the current is 2 A. If we add another identical resistor into the circuit in parallel, the total current will become _________ A • A circuit has one resistor and the current is 2 A. If we add another 3 identical resistors into the circuit in parallel, the current will become _________ A Parallel Circuits Exercise • Calculate the total resistance R and total current I 10 Ω 20 Ω I + 3.0 V – Parallel Circuits Exercise • Calculate and compare I1 and I2 I 10 Ω I1 40 Ω I2 + 10 V – Parallel Circuits Exercise • Calculate the equivalent resistance and voltage V of the cell 40 Ω 80 Ω 0.1 A + V – Parallel Circuits Exercise • Calculate the resistance R 300 Ω R 0.2 A + 3.0 V – Parallel Circuits Exercise • If the current for the 10 Ω resistor is 2 A, calculate the voltage V of the cell and the 10 Ω 2A total current I 40 Ω I + V – Parallel Circuits Exercise • Calculate the Power P1, P2, and total power P of the circuit 10 Ω 40 Ω I P1 P2 + 10 V – Parallel Circuits Exercise • Calculate all the unknown quantities in the diagram 200 Ω 400 Ω I + V1 – I1 + V2 – I2 + 3V – Parallel Circuits • What will happen to the circuit if we cut a wire of the circuit? Parallel Circuits • What is the disadvantage of the parallel circuits? Parallel Circuits • What is the disadvantage of the parallel circuits? When more branches are added, a greater amount of total current occurs in the line and can be over its safe amount – overload Sometimes, it requires more wires Compound Circuits Equivalent Resistance • The value of a single resistor that would comprise the same load of several resistors in its network to the battery or power source Equivalent Resistance of Series Circuits • What’s the equivalent resistance? R1 + V1 – R2 + V2 – I1 I2 I R3 + V + – V3 – I3 Rn + Vn – In Equivalent Resistance of Series Circuits • What’s the equivalent resistance? Req = R1 + R2 + R3+ …… + Rn R1 + V1 – R2 + V2 – I1 I2 I R3 + V + – V3 – I3 Rn + Vn – In Equivalent Resistance of Series Circuits • What’s the equivalent resistance? V1 – I1 V R2 + 2 – I2 V3 – I3 R1 + R3 + ……… Rn I + Vn – + V – In Equivalent Resistance of Series Circuits • What’s the equivalent resistance? V1 – I1 V R2 + 2 – I2 V3 – I3 R1 + 1/Req = 1/R1 + 1/R2 + …… + 1/Rn R3 + ……… Rn I + Vn – + V – In Compound Circuits • The equivalent resistor of a compound circuit can be found by combining resistors in series and in parallel Compound Circuits R1 R3 R2 R 1-2 R3 R 1-2-3 Compound Circuits • The equivalent resistor of a compound circuit can be found by combining resistors in series and in parallel Compound Circuits R2 R1 R3 R 1-2 R3 R 1-2-3 Compound Circuits Example • Calculate the equivalent resistance of the following compound circuit 2Ω 3Ω 2Ω Compound Circuits Example • Calculate the equivalent resistance of the following compound circuit R1 = 2 Ω R1-2 = R1R2 /(R1+R2) R1-2 = 22/(2+2) Ω= 1 Ω R1-2-3 = R1-2 +R3 R1-2-3 = 1 Ω + 3 Ω = 4 Ω R2 = 2 Ω R3 = 3 Ω Compound Circuits Example • Calculate the equivalent resistance R and the total current I 2Ω 1Ω 4Ω 7V Compound Circuits Example • Calculate the equivalent resistance R and the total current I R1-2 = R1R2 /(R1+R2) R1-2 = 24/(2+4) Ω= 4/3 Ω R = R1-2 +R3 R = 4/3 Ω + 1 Ω = 7/3 Ω I = V/R = 7 V / (7/3 Ω) =3A R1 = 2 Ω R3 = 1 Ω R2 = 4 Ω 7V Compound Circuits Exercise • Calculate the equivalent resistance R and the total current I 10 Ω 20 Ω 15 Ω 30 Ω 12 V Compound Circuits Exercise • Calculate the the total current I and total voltage V 0.1 A 10 Ω 20 Ω 15 Ω 30 Ω I V Compound Circuits Exercise • If R1 = R2, calculate the R1, I2 , and the total current I R1 I2 R2 + 10 V – + 4V – 40 Ω Electric Circuits Electric Circuit Symbols