# Combination Circuits. Simplifying Resistors in Combination Circuits 3©3© 11©

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Combination Circuits Slide 2 Simplifying Resistors in Combination Circuits 33 11 Slide 3 4 18 Slide 4 4 18 Slide 5 Combo Circuits Quiz Slide 6 Now we can analyze other aspects of a circuitin order to do this we must first simplify. R 1 = 1 R 2 = 8 R 3 = 8 1 = 1 + 1 R 2,3 R 2 R 3 1 = 1 + 1 = 2 = 4 R 2,3 8 8 8 R 1 = 1 R 2,3 = 4 100 V 0 V 100 V0 V Slide 7 Next simplified the circuit down to one resistor. R 1 = 1 R 2,3 = 4 100 V0 V Series = R T = R 1 + R 2,3 R T = 1 + 4 R T = 5 100 V0 V Slide 8 We went from R 1 = 1 R 2 = 8 R 3 = 8 100 V 0 V to R 1 = 1 R 2,3 = 4 100 V0 V to R T = 5 100 V0 V Slide 9 Next find the total current flowing through the simplified circuit. R T = 5 100 V0 V I T = V T R T I T = 100 V 5 I T = 20 A Now we can go back and un-simplify the circuit and find the current and voltage through specific resistors Slide 10 Find the current and voltage through R 1. Hint: Always find current first, then voltage. R 1 = 1 R 2,3 = 4 100 V0 V R T = 5 100 V0 V We already found the current through R T and since this is a series circuit I T = I 1 = I 2,3 so I 1 = 20 A. Next find voltage Slide 11 R 1 = 1 R 2,3 = 4 100 V0 V I 1 = 20 AI 2,3 = 20 A V 1 = I 1 R 1 In a series circuit V T = V 1 + V 2,3 so the voltages across both of these resistors will add up to 100 V. V 1 = (20A)( 1 ) V 1 = 20 V V 2,3 = I 2,3 R 2,3 V 2,3 = (20A)( 4 ) V 2,3 = 80 V Lets check to see if the voltages make sense: V T = V 1 + V 2,3 100 V = 20 V + 80 V Slide 12 Now we can find the separate currents and voltages through R 2 and R 3. R 1 = 1 R 2,3 = 4 100 V0 V I 1 = 20 AI 2,3 = 20 A R 1 = 1 R 2 = 8 R 3 = 8 100 V 0 V I 1 = 20 A I 2,3 = 20 A Slide 13 R 1 = 1 R 2 = 8 R 3 = 8 100 V 0 V I 1 = 20 A I 2,3 = 20 A R 2 and R 3 are in parallel so we know that V 2,3 = V 2 = V 3 therefore V 2 and V 3 are 80 V. Now we can find I 2 and I 3. I 2 = V 2,3 R 2 I 2 = 80 V 8 I 2 = 10 A I 3 = V 2,3 R 3 I 3 = 80 V 8 I 3 = 10 A V 1 = 20 V V 2,3 = 80 V Slide 14 Lets try another one R 3 = 6 R 1 = 4 R 2 = 2 Resistors R 1 and R 2 are in series so R 1,2 = R 1 + R 2 R 1,2 = R 1 + R 2 R 1,2 = 4 + 2 = 6 R 3 = 6 R 1,2 = 6 100 V0 V 100 V0 V Slide 15 R 3 = 6 R 1,2 = 6 100 V0 V 1 = 1 + 1 R T R 1,2 R 3 1 = 1 + 1 = 2 = 3 R T 6 6 6 R T = 3 100 V0 V Slide 16 R 3 = 6 R 1 = 4 R 2 = 2 100 V0 V R 3 = 6 R 1,2 = 6 100 V0 V R T = 3 100 V0 V Slide 17 What do we do next? R T = 3 100 V0 V I T = V T R T I T = 100 V 3 I T = 33.33 A Next we un-simplify the circuit and find the rest Slide 18 R 3 = 6 R 1,2 = 6 100 V0 V I T = 33.33 A Since R 1,2 and R 3 are in parallel they have voltage in common: V T = V 1,2 = V 3 therefore V 1,2 and V 3 are both 100 V. We can now find each resistors individual current flow, I T = I 1,2 + I 3. I 1,2 = V 1,2 R 1,2 I 1,2 = 100 V 6 I 1,2 = 16.67 A I 3 = V 3 R 3 I 3 = 100 V 6 I 3 = 16.67 A Slide 19 Now lets separate R 1 and R 2 R 3 = 6 R 1,2 = 6 100 V0 V R 3 = 6 R 1 = 4 R 2 = 2 100 V0 V I 3 = 16.67 A I 1,2 = 16.67 A Slide 20 R 3 = 6 R 1 = 4 R 2 = 2 100 V0 V I 3 = 16.67 A I 1,2 = 16.67 A R 1 and R 2 are in series with each other so they have the same amount of current flowing through them: I 1,2 = I 1 = I 2 therefore the current flowing through both of them is 16.67 A which will help us find the voltage drop across each resistor. V 1 = I 1,2 R 1 V 1 = (16.67A)( 4 ) V 1 = 66.68 V V 2 = I 1,2 R 2 V 2 = (16.67A)( 2 ) V 2 = 33.34 V Slide 21 Lets try another R 1 = 2 R 2 = 4 R 3 = 4 21 V 0 V R 4 = 3 Remember the steps: 1. Simplify the circuit so that there is only 1 resistor. 2. Find the total current of the simplified resistor. 3. Work backward, un-simplifying the circuit, finding the current and voltage of each resistor along the way. 4. Be sure to do this using the correct equations that go with that section of the circuit. Slide 22 1. Simplify the circuit so that there is only 1 resistor. R 1 = 2 R 2 = 4 R 3 = 4 21 V 0 V R 4 = 3 R T = 7 21 V0 V R 1 = 2 21 V0 V R 2,3 = 2 R 4 = 3 Slide 23 2. Find the total current of the simplified resistor. R T = 7 21 V0 V I T = V T R T I T = 21 V 7 I T = 3 A Slide 24 3. Work backward, un-simplifying the circuit, finding the current and voltage of each resistor along the way. R T = 7 21 V0 V R 1 = 2 21 V0 V R 2,3 = 2 R 4 = 3 I 1 = 3 A I 2,3 = 3 A I 4 = 3 A V 1 = I 1 R 1 V 1 = (3 A)( 2 ) V 1 = 6 V V 2,3 = I 2,3 R 2,3 V 2,3 = (3 A)( 2 ) V 2,3 = 6 V V 4 = I 4 R 4 V 4 = (3 A)( 3 ) V 4 = 9 V Slide 25 R 1 = 2 21 V0 V R 2,3 = 2 R 4 = 3 I 1 = 3 A I 2,3 = 3 A I 4 = 3 A V 1 = 6 VV 2,3 = 6 VV 4 = 9 V R 1 = 2 R 2 = 4 R 3 = 4 21 V 0 V R 4 = 3 V 2 = 6 V V 3 = 6 V I 2 = V 2 R 2 I 2 = 6 V 4 I 2 = 1.5 A I 3 = V 3 R 3 I 3 = 6 V 4 I 3 = 1.5 A I 2,3 = 3 A Slide 26 Lets try another R 1 = 1 R 2 = 3 R 4 = 6 30 V 0 V R 5 = 1 Remember the steps: 1. Simplify the circuit so that there is only 1 resistor. 2. Find the total current of the simplified resistor. 3. Work backward, un-simplifying the circuit, finding the current and voltage of each resistor along the way. 4. Be sure to do this using the correct equations that go with that section of the circuit. R 3 = 3 Slide 27 R 1 = 1 R 2 = 3 R 4 = 6 30 V 0 V R 5 = 1 R 3 = 3 R 1 = 1 R 2,3 = 6 R 4 = 6 30 V 0 V R 5 = 1 R T = 5 30 V0 V R 1 = 1 30 V0 V R 2,3,4 = 3 R 5 = 3 Slide 28 More practice a)Which letter shows the graph of voltage vs. current for the smallest resistance? b) Which letter shows the graph of voltage vs. current for the largest resistance? Slide 29 a)What is the total resistance of this circuit? b) What is the total current of this circuit? c) What is the amount of current running through each resistor? Slide 30 a) What is the total resistance of this circuit? b) What is the total current of this circuit? Slide 31 a) Find the equivalent resistance. b) Find the current (I T ) going through this circuit. c) Find potential drop across R 1 & R 2 Slide 32 a) Find combined resistance (R T ). b) Find the current in R 1. c) Find I 3. d) Find R 2. e) Find value of the second resistor. Slide 33 a)If the voltage drop across the 3 ohm resistor is 4 volts, then what would the voltage drop be across the 6 ohm resistor? b) Find the total voltage in this series circuit. c) Find combined resistance in this circuit. d) Find the total current in this circuit. Slide 34 a) Current in this circuit? b) Potential difference in 20 ohm resistor? c) Equivalent resistance in the circuit? Slide 35 Find R 2.