Series and Parallel Circuits When devices are connected in an electric circuits, they can be connected in “series” or in “parallel” with other devices. When devices are series, any current that goes through one device must also go through the other devices. For example: Series Connection 1 2 A B The devices, numbered “1” and “2” in the diagram above, are connected in series. If an electron (or even conventional positive current) needs to move from point A to point B, it must go through both device 1 and device 2. Everything that goes through one must also go through the other.

Series and Parallel Circuits When devices are connected in an electric circuits, they can be connected in “series” or in “parallel” with other devices. When devices are parallel, the current goes through one device only. For example: Parallel Connection 1 2 A B The devices, numbered “1” and “2” in the diagram above, are connected in parallel. If an electron (or even conventional positive current) needs to move from point A to point B, it must go through only one device, not both. Some current goes through one, some through the other.

Resistors in Series Resistors in Parallel 1 2 A B If devices 1 and 2 are resistors, think of the series connection as a longer resistor. Longer resistors have greater resistance. The total resistance of a combination of resistors in series is greater than any of the individual resistances. Resistors in Parallel 1 2 A B If devices 1 and 2 are resistors, think of the parallel connection as a wider resistor. Wider resistors have lower resistance. The total resistance of a combination of resistors in paralle is smaller than any of the individual resistances.

Series Circuits V R2 R1 R3 The schematic circuit diagram to the right shows three resistors (R) connected in series with a source of potential difference (V). Rules for a simple series circuit…. (in sentence form) 1) The total equivalent resistance of resistors in series is equal to the sum of the individual resistances. 2) The sum of the voltage drops across each of the resistors is equal to the total voltage of the power supply. 3) The same amount of current flows through all the resistors. 4) The total power converted by the three resistors is equal to the sum of the individual powers

Rules for a simple series circuit…. (in equation form) Series Circuits V R2 R1 R3 The schematic circuit diagram to the right shows three resistors (R) connected in series with a source of potential difference (V). Rules for a simple series circuit…. (in equation form) Req = R1 + R2 + R3 +... V = V1 + V2 + V3 + ... I = I1 = I2 = I3 = ... P = P1 + P2 + P3 + ...

Parallel Circuits R3 V R1 R2 The schematic circuit diagram to the right shows three resistors (R) connected in parallel with a source of potential difference (V). Rules for a simple parallel circuit…. (in sentence form) 1) The reciprocal of the total equivalent resistance of resistors in series is equal to the sum of the reciprocals of the individual resistances. 2) All of the resistors have the same voltage drop across them. 3) The sum of the currents through all the parallel resistors is equal to the total current supplied by the voltage source. 4) The total power converted by the three resistors is equal to the sum of the individual powers.

Parallel Circuits R3 V R1 R2 The schematic circuit diagram to the right shows three resistors (R) connected in parallel with a source of potential difference (V). Rules for a simple parallel circuit…. (in equation form) V = V1 = V2 = V3 = …. I = I1 + I2 + I3 +…. P = P1 + P2 + P3 + ….

Series Circuits: Example Problem V = 24 V R2 = 4 W R1 = 2 W R3 = 6 W Req = R1 + R2 + R3 +… V = V1 + V2 + V3 + … I = I1 = I2 = I3 = … P = P1 + P2 + P3 + ... Fill in Given Use Req = R1 + R2 + R3 +… to find the total equivalent resistance. 1 V I R P 2 3 T Use V = IR to find the total current 2 4 6 24 4 8 12 2 8 16 24 48 I = I1 = I2 = I3 = … Use V = IR to find the individual voltages Use P = VI to find all the powers 2 12

Parallel Circuits: Example Problem V = V1 = V2 = V3 = ... I = I1 + I2 + I3 + ... P = P1 + P2 + P3 = ... V = 50 V R1 = 20 W R2 = 25 W R3 = 100 W Fill in Given V = V1 = V2 = V3 = ... Use to find the total equivalent resistance. 1 V I R P 2 3 T 20 25 100 50 50 2.5 2 0.5 5 125 100 25 250 Use V = IR to find the individual currents Use P = VI to find all the powers 10

Combination Circuits Now R2 is in parallel with R4, 3. V R1 R2 R4 R6 R5 The circuit to the right is a complicated combination circuit. The resistors aren’t all in series or all in parallel. To analyze a combination circuit, first look for pairs (or more) of resistors which are in series or parallel. In this example R3 and R4 are in series, while R5 and R6 are in parallel. Use the series and parallel rules to replace the pairs with “equivalent” resistors. V R1 R2, 3, 4 R5, 6 V R1, 2, 3, 4, 5, 6 V R1 R2 R4, 3 R5, 6 Now R2 is in parallel with R4, 3. Now R2, 3, 4 is in series with R1 and R5, 6.

Combination Circuits R3 = 12 W V = 120 V R1 = 19 W R2 = 48 W R4 = 12 W R6 = 30 W R5 = 6 W Example: Find the equivalent resistance of the six resistors in the circuit at right. 1/R5,6 = 1/R5 + 1/R6 = 1/30W + 1/6 W R5,6 = 5 W R3,4 = R3 + R4 = 12 W + 12 W R3,4 = 24 W 1/R2,3,4 = 1/R2 + 1/R3,4 = 1/48W + 1/24W R2,3,4 = 16 W R1,2,3,4,5,6 = R1 + R2,3,4 + R5,6 R1,2,3,4,5,6 = 19 W + 16 W + 5 W R1,2,3,4,5,6 = 40 W

Combination Circuits: Finding Equivalent Resistance

Combination Circuits: Hints When the current reaches point A, it must split to the right or the left. If R1 has a bigger resistance than R2, most of the current will go through R2. If R1 = 2 x R2, then twice as much current will go through R2 as compared to R1. I1 + I2 = I 2 x I1 = I2 I1 = (1/3)I I2 = (2/3)I R2 R1 A B Answer: If R1 = 5 x R2, then five times as much current will go through R2 as compared to R1. I1 + I2 = 30 A 5 x I1 = I2 I1 = (1/6)(30 A) = 5 A I2 = (5/6)(30 A) = 25 A R1 = 50 W R2= 10 W A B I = 30 A Example Problem: How much of the 30 A of current goes through each resistor in the diagram at right?

Combination Circuits Q: Put them in order from brightest to dimmest: Example Problem: The circuit to the right represents a battery and four identical light bulbs connected in a combination circuit. Q: Put them in order from brightest to dimmest: Brightest: R4 (all current goes through it) 2nd R1 (gets 2/3 of total current) 3rd & 4th R2 and R3 (get 1/3 of total current) R2 R1 R3 R4

Combination Circuits Now the bulb represented by R3 is unscrewed from its socket. R2 R1 R3 R4 Q: What happens to the brightness of the other three bulbs? R2 goes out (no current through that branch) R4 gets dimmer (fewer current paths = more total resistance in circuit = less total current = less through R4) R1 gets brighter (current through R4 decreases, voltage across R4 decreases, voltage across R1 increases = it gets less bright)

Combination Circuits R3 V R1 R2 R4 R6 R5 R7 R8 R9 R10 The circuit to the right consists of ten identical resistors. Put the resistors in order from the greatest amount of current to the least current. Answer: Most current: R1 (only resistor which all the current passes through) 2nd: R2 (gets 2/3 of the total current) 3rd: R5 and R6 (get 1/2 of the total current) 4th: R3 and R4 (get 1/3 of the total current) Last: R7, R8, R9, R10 (get 1/4 of total current)