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Circuits Answer Me!!! What is required for electricity to flow? Circuit Elements A circuit must have A source of potential difference (battery) A source of resistance (resistor) Wires connecting both terminals of the potential difference source A circuit may have Switches Multiple resistors Voltmeters or Ammeters connected Circuit Symbols Be sure to check your reference tables for appropriate symbols to use in circuit diagrams. Ammeters & Voltmeters Ammeter Measures Current Connected in Series Low Resistance Voltmeter Measures Potential Diff Connected in Parallel High Resistance Types of Circuits There are two types of circuits: Series circuits – have only 1 path for current to flow. Parallel circuits – have multiple paths for current to flow. Series Circuits The current flows from the battery to R1 through R2 and then through R3 then back to the battery. Current in a Series Circuit In a series circuit current is the same through all parts of the circuit. That means that the current coming from the battery is equal to the current through any resistor. Itotal = I1 = I2 = I3 = … Potential Difference in a Series Circuit The potential difference provided by the battery is equal to the sum of the potential differences across each resistor in the circuit. Vtotal = V1 + V2 + V3 + … Note that potential difference for each resistor is consistent with Ohm’s Law. Resistance in a Series Circuit Ohm’s Law States: V R I So, Vtotal Rtotal I total And therefore: V1 V2 V3 ... V1 V2 V3 Rtotal R1 R2 R3 I total I I I Rtotal = R1 + R2 + R3 + … Practice Problem 1 The diagram below shows resistors R1, R2 and R3 connected to a 12V battery. If the voltage across R1 is 3V and the voltage across R2 is 4V, what is the potential difference across R3? 3V 4V 12 V Practice Problem 2 R1 = 100W; R2 = 12W; and R3 = 4W in a series circuit. Find the total (equivalent) resistance. Practice Problem 3 The diagram shows a circuit with two resistors. What is the reading on the ammeter? Practice Problem 4 A 30 ohm and 60 ohm resistors are connected in series to 12 V battery. Compared to the current through the 30 ohm resistor, the current through the 60 ohm resistor is Smaller Larger The same Practice Problem 5 Determine the reading of the voltmeter. Practice Problem 6 At what value must the variable resistor be set to produce a current of 1.0 A through R1? Practice Problem 7 What is the reading of voltmeter V1? Practice Problem 8 A 100 ohm resistor and an unknown resistor are connected in series to a 10V battery. If the potential drop across the 100 ohm resistor is 4 V, what is the resistance of the unknown resistor? Answer Me!!! What makes a circuit a parallel circuit? Parallel Circuits Current can flow from the battery to either R1, R2 or R3 and then back to the battery. Current will take the path of least resistance. Current in a Parallel Circuit In a parallel circuit, total current equals the sum of all the currents in the circuit (current through each parallel path). Itotal = I1 + I2 + I3 + … Potential difference in Parallel Circuits In a parallel circuit, the potential difference is the same in all parts of the circuit and is also the same as the total voltage (from the battery). Vtotal = V1 = V2 = V3 = … Resistance in a Parallel Circuit Using Ohm’s law, we see: V Req I1 I 2 I 3 ... Also stated as: 1 1 1 1 ... Req R1 R2 R3 Note that Req is always less than any individual resistance in a parallel circuit. Conservation of Charge in Electric Circuits Charge in an electric circuit must be conserved. At any junction in a circuit, the sum of the currents entering the junction must equal the sum of the currents leaving. Practice Problem The diagram below shows currents in a segment of an electric circuit. Draw the direction and label the magnitude of the current through A. 8A 3A 4A A Practice Problem 9 What are the correct readings of the two voltmeters? Practice Problem 10 What is the total resistance of this circuit segment? Practice Problem 11 What is the total (equivalent) resistance of the following circuit? Practice Problem 12 Two identical resistors connected in parallel have an equivalent resistance of 40 ohms. What is the resistance of each resistor? Practice Problem 13 Resistors R1 and R2 have and equivalent resistance of 6W when connected in parallel. The resistance of R1 could be: 1W 5W 8W 4W Answer Me!!! What is the current measured by ammeter A? Practice Problem 15 What is the current reading of ammeter A? Answer Me!!! Draw a series circuit that has 3 resistors. Then draw a properly connected ammeter to measure the total current and a properly connected voltmeter to measure the potential drop across resistor 1.