CK-12 Physics Concepts - Intermediate Answer Key Chapter 19: Electrical Circuits 19.1 Series Circuits Review Questions 1. There are three 20.0 Ohm resistors connected in series across a 120 V generator. a. What is the total resistance of the circuit? b. What is the current in the circuit? c. What is the voltage drop across one of the resistors? 2. A 5.00Ω, a 10.0Ω, and a 15.0Ω resistor are connected in a series across a 90.0 V battery. a. What is the equivalent resistance of the circuit? b. What is the current in the circuit? c. What is the voltage drop across the 5.00Ω resistor? 3. A 5.00Ω and a 10.0Ω resistor are connected in series across an unknown voltage. The total current in the circuit is 3.00 A. a. What is the equivalent resistance of the circuit? b. What is the current through the 5.00Ω resistor? c. What is the total voltage drop for the entire circuit? Answers 1. a. Using 푅푇 = 푅1 + 푅2 + 푅3 ∶ 20Ω + 20Ω + 20Ω = 60Ω ∶ 퐑퐓 = ퟔퟎ훀 푉 120푉 b. Using 퐼 = ∶ = ퟐ푨 푅 60Ω c. Using 푉 = 퐼푅 ∶ (2퐴)(20Ω) = ퟒퟎ푽 (this is the same for each resistor) 2. a. Using 푅푇 = 푅1 + 푅2 + 푅3 ∶ 5Ω + 10Ω + 15Ω = 30Ω ∶ 퐑퐓 = ퟑퟎ훀 푉 90푉 b. Using 퐼 = ∶ = ퟑ푨 푅 30Ω c. Using 푉 = 퐼푅 ∶ (3퐴)(5Ω) = ퟏퟓ푽 3. a. Using 푅푇 = 푅1 + 푅2 ∶ 5Ω + 10Ω = 15Ω ∶ 퐑퐓 = ퟏퟓ훀 1 푉 45푉 b. Using 퐼 = ∶ = ퟑ푨 푅 15Ω c. Using 푉 = 퐼푅 ∶ (3퐴)(15Ω) = ퟒퟓ푽 19.2 Parallel Circuits Review Questions 1. Three 15.0Ω resistors are connected in parallel and placed across a 30.0 V potential difference. a. What is the equivalent resistance of the parallel circuit? b. What is the total current through the circuit? c. What is the current through a single branch of the circuit? 2. A 12.0Ω and a 15.0Ω resistor are connected in parallel and placed across a 30.0 V potential. a. What is the equivalent resistance of the parallel circuit? b. What is the total current through the circuit? c. What is the current through each branch of the circuit? 3. A 120.0Ω resistor, a 60.0Ω resistor, and a 40.0Ω resistor are connected in parallel and placed across a potential difference of 12.0 V. a. What is the equivalent resistance of the parallel circuit? b. What is the total current through the circuit? c. What is the current through each branch of the circuit? Answers 1. 1 1 1 1 1 1 1 1 1 3 a. Using = + + … ∶ = + + ∶ = ∶ 푹푻 = ퟓ훀 푅푇 푅1 푅2 푅3 푅푇 15Ω 15Ω 15Ω 푅푇 15Ω b. Using 퐼푇 = 퐼1 + 퐼2 + 퐼3 … 푉푇 푉푇 푉푇 30.0푉 30.0푉 30.0푉 퐼푇 = ( ) + ( ) + ( ) = ( ) + ( ) + ( ) : 푰푻 = ퟔ푨 푅1 푅2 푅3 15Ω 15Ω 15Ω 푉 30.0푉 c. Using 퐼 = ∶ 퐼 = ∶ 푰 = ퟐ푨 푅 15Ω 2. 1 1 1 1 1 1 1 3 a. Using = + + … ∶ = + = ∶ 푹푻 = ퟔ. ퟔퟕ훀 푅푇 푅1 푅2 푅3 푅푇 12Ω 15Ω 20Ω b. Using 퐼푇 = 퐼1 + 퐼2 + 퐼3 … 푉푇 푉푇 푉푇 30.0푉 30.0푉 퐼푇 = ( ) + ( ) + ( ) = ( ) + ( ) : 푰푻 = ퟒ. ퟓ푨 푅1 푅2 푅3 12Ω 15Ω 2 푉 c. Using 퐼 = 푅 30.0푉 퐼 = ∶ 푰 = ퟐ. ퟓ푨 1 12Ω ퟏ 30.0푉 퐼 = ∶ 푰 = ퟐ푨 2 15Ω ퟐ 3. 1 1 1 1 1 1 1 1 1 1 a. Using = + + … ∶ = + + ∶ = ∶ 푹푻 = ퟐퟎ훀 푅푇 푅1 푅2 푅3 푅푇 120.0Ω 60.0Ω 40Ω 푅푇 20Ω b. Using 퐼푇 = 퐼1 + 퐼2 + 퐼3 … 푉푇 푉푇 푉푇 12.0푉 12.0푉 12.0푉 퐼푇 = ( ) + ( ) + ( ) = ( ) + ( ) + ( ) : 푰푻 =. ퟔ푨 푅1 푅2 푅3 120Ω 60Ω 40Ω 푉 c. Using 퐼 = ∶ 푅 12.0푉 퐼 = ∶ 푰 =. ퟏ푨 1 120Ω ퟏ 12.0푉 퐼 = ∶ 푰 =. ퟐ푨 2 60Ω ퟐ 12.0푉 퐼 = ∶ 푰 =. ퟑ푨 3 40Ω ퟑ 19.3 Combined Series-Parallel Circuits Review Questions 1. Two 60.0Ω resistors are connected in parallel and this parallel arrangement is then connected in series with a 30.0Ω resistor. The combination is then placed across a 120. V potential difference. a. Draw a diagram of the circuit. b. What is the equivalent resistance of the parallel portion of the circuit? c. What is the equivalent resistance for the entire circuit? d. What is the total current in the circuit? e. What is the voltage drop across the 30.0Ω resistor? f. What is the voltage drop across the parallel portion of the circuit? g. What is the current through each resistor? 2. Three 15.0 W resistors are connected in parallel and the combination is then connected in series with a 10.0 W resistor. The entire combination is then placed across a 45.0 V potential difference. Find the equivalent resistance for the entire circuit. 3 Answers 1. a. 1 1 1 1 b. Using = + = ∶ 푹ퟐ ퟑ = ퟑퟎ훀 푅2 3 60Ω 60Ω 30Ω c. Using 푅푇 = 푅1 + 푅2 3 = 30Ω + 30Ω ∶ 푹푻 = ퟔퟎ훀 푉푇 120.푉 d. Using 퐼푇 = = ∶ 푰푻 = ퟐ푨 푅푇 60Ω e. Voltage drop across the 30 Ohm resistor = (30Ω)(2퐴) = ퟔퟎ푽 f. Voltage drop across parallel portion = 120푉 − (푑푟표푝 푎푐푟표푠푠 푠푒푟푖푒푠 푝표푟푡푖표푛) = 60푉 푉 g. Current through each resistor may be found using 퐼 = : 푅 ퟔퟎ푽 푰 = = ퟐ푨 (same as total current, as it should be) ퟏ ퟑퟎ훀 ퟔퟎ푽 푰 = = ퟏ푨 ퟐ ퟔퟎ훀 ퟔퟎ푽 푰 = = ퟏ푨 ퟑ ퟔퟎ훀 2. Equivalent resistance for the entire circuit is equal to the equivalent resistance of the series circuit including the 10 Ohm resistor and the equivalent resistance of the three 15 Ohm resistors. Start with the three 15 Ohm resistors in parallel: 1 1 1 1 1 1 1 1 Using = + + = + + = ∶ 푹푻풑풂풓풂풍풍풆풍 = ퟓ훀 푅푇푝푎푟푎푙푙푒푙 푅1 푅2 푅3 15Ω 15Ω 15Ω 5Ω Using the series resistance formula with the 10Ohm resistor and the equivalent parallel resistance of 5Ohms: 푅푇 = 푅1 + 푅2 ∶ 10Ω + 5Ω = 15Ω The equivalent resistance for the entire circuit is ퟏퟓ훀. 4 19.4 Ammeters and Voltmeters Review Questions [3] 1. In the sketch at above, there are four positions available for the placement of meters. Which position(s) would be appropriate for placement of an ammeter? a. 1 b. 3 c. 4 d. All of them. e. None of them. 2. Which position(s) would be appropriate for placement of a voltmeter? a. 1 b. 2 c. 3 d. All of them. e. None of them. 3. Which position could hold an ammeter that would read the total current through the circuit? a. 1 b. 2 c. 3 d. 4 e. None of them. 4. Which position could hold a voltmeter that would read the total voltage drop through the circuit? a. 1 b. 2 c. 3 or 4 d. All of them. e. None of them. Answers 1. Answer a : Position 1 (The only position offered where the ammeter would be connected in series) 5 2. Answer c : Position 3 (The only position offered where the voltmeter would be connected in parallel) 3. Answer a : Position 1 (This position is in series, and is not on a section of the circuit that is in parallel with another section) 4. Answer e : None of these (None of the indicated positions would place the voltmeter in parallel over the entire circuit. An enterprising student could certainly calculate the drop using positions 3 and 4, however.) 6 .