Combining Resistors Objective: To work out the total equivalent resistance of a multiple of resistors in a circuit. Starter quiz

V3 V V2 V1 9V 2V ?V M NP What would the reading on V3 be? a.3V b.5V c.7V d.9V

Which meter is in the wrong place? a. A1, A2 & A3 b. A2 & A3 c. V1 & V2 d. V3 A2 A1 V2 A3 V3 V1

Which meter is in the wrong place? a. A1, A2 & A3 b. A2 & A3 c. V1 & V2 d. V3 A2 A1 V2 A3 V3 V1

6A Circuit W A What is a possible reading for the ammeter in circuit Z? a.0A b.3A c.6A d.12A ?A Circuit Z A 4Ω 2Ω

6A Circuit W A What is the voltage across the 4Ω resistor? a.24 V b.10V c.6V d.1.5 V 4Ω

6A 12V A What is the value of the resistance in the circuit? a.0Ω b.2Ω c.6Ω d.12Ω ?Ω

What is the voltage supplied by the cell in this circuit? a.4V b.16V c.32V d.64V 2A A 8Ω ??? V

12V 4 Ω The current from the battery is 6A, how much is the current through the 4Ω resistor ? 6A

12V 4 Ω The current from the battery is 6A, how much is the current through the 4Ω resistor ? 6A 3A

12V 3 Ω 6 Ω A 3Ω resistor and a 6Ω connected in parallel. Which resistor passes the most current ?

12V 3 Ω 6 Ω A 3Ω resistor and a 6Ω connected in parallel. Which resistor passes the most current ? The 3Ω resistor

A B C Circuit 1 which bulb will light up (notice the position of the diodes).

A B C answer Circuit 1 A & B only

A B C Circuit 2 which bulb will light up (notice the position of the diodes).

A B C answer Circuit 2 None of them

A B C Circuit 3 which bulb will light up (notice the position of the diodes).

A B C answer Circuit 3 A & C only

Voltage (V) Current (A) Voltage (V) Current (A) Voltage (V) Current (A) A B C Which of the following current-voltage graphs is of light bulb ? Last q

Voltage (V) Current (A) Voltage (V) Current (A) Voltage (V) Current (A) A B C Which of the following current-voltage graphs is of light bulb ? Last q

Combining Resistors Objective: To work out the total equivalent resistance of a multiple of resistors in a circuit.

Combining Resistors The total resistance R T of any number of resistors R1, R2, R3, …. connected in series is given by the formula: R T = R 1 + R 2 + R 3 + ……. 6Ω 4Ω Resistors in series: Example: A 6Ω resistor in series with a 4Ω resistor are equivalent to a 10Ω resistor. Resistors in parallel: The total resistance R T of any number of resistors R1, R2, R3, …. connected in parallel is given by the formula: RTRT 1 = R1R1 1 + R2R2 1 R3R ….. Example: A 6Ω resistor in parallel with a 4Ω resistor are equivalent to : 6Ω 4Ω RTRT 1 = R1R1 1 + R2R2 1 = = R T = 1 / = 2.4Ω Next: proof R1 R2 R1 R2

RTRT Where did this equation come from? RTRT = R1R1 + R2R2 V I Next: parallel In series R1R1 V I R2R2 Voltage from the cell is shared between the components: V = V 1 + V 2 IR T = IR 1 + IR 2 R T = R 1 + R 2 I I

R1 R2 RTRT Where did this equation come from? V I I1 I2 RTRT 1 = R1R1 1 + R2R2 1 V I I = I1 + I2 Since voltage is the same in any closed loop, V = V 1 = V 2 RTRT V = R1R1 V1V1 + R2R2 V2V2 RTRT 1 = R1R1 1 + R2R2 1 Next: example In parallel

Example 20Ω 30Ω RTRT Find the equivalent resistor that can replace two resistors in parallel: R 1 = 20Ω, R 2 = 30Ω = R T = 12Ω RTRT 1 = R1R1 1 + R2R2 1 RTRT 1 = RTRT 1 Next: investigation For the mathematically challenged beings: if the combination had only two resistors in parallel, then: R T = R 1 R 2 / (R 1 +R 2 ) or ‘product over sum’. This can save the faint-hearted from reciprocals!

Investigating resistors in series and parallel

Investigating resistors in series and parallel (20 min) Use the Ohmmeter to measure the resistance of resistor X, Y, Z Use resistors X, Y and Z to create the different combinations shown below. X = ………… Ω Y = ………… Ω Z = ………… Ω XY X YZX Z Y Z X Z Y CombinationPredicted equivalent resistance / Ω Measured equivalent resistance / Ω

Investigating resistors in series and parallel Use the Ohmmeter to measure the resistance of resistor X, Y, Z Use resistors X, Y and Z to create the different combinations shown below. X = ………… Ω Y = ………… Ω Z = ………… Ω XY X YZX Z Y Z X Z Y CombinationPredicted equivalent resistance / Ω Measured equivalent resistance / Ω 15 Ω 35 Ω 4 Ω 6.7 Ω 8.6 Ω Next: plenary

a.40Ω b.90 Ω c.65 Ω d.140 Ω 40Ω 50Ω What is R T ?

a.40Ω b.132 Ω c.25 Ω d.67 Ω 40Ω 50Ω 100Ω 200Ω What is R T ?

a.50 Ω b.132 Ω c.25 Ω d.63 Ω 10Ω What is R T ? 20Ω 40Ω 15Ω 25Ω

a.450 Ω b.532 Ω c.500 Ω d.600 Ω 100Ω What is R T ? 200Ω 100Ω

a.110 Ω b.50 Ω c.45 Ω d.55 Ω 40Ω What is R T ? 50Ω 70Ω 30Ω

a.50 Ω b.20 Ω c.5 Ω d.1 Ω 20Ω What is R T ? 10Ω Last q

Combining Resistors Objective: To work out the total equivalent resistance of a multiple of resistors in a circuit.