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 π π = π 1 + π 2 + π 3 βΆ 20Ω + 20Ω + 20Ω = 60Ω βΆ π π = πππ π b. Using πΌ = π βΆ 120π 60Ω = ππ¨ c. Using π = πΌπ βΆ (2π΄)(20Ω) = πππ½ (this is the same for each resistor) 2. a. Using π π = π 1 + π 2 + π 3 βΆ 5Ω + 10Ω + 15Ω = 30Ω βΆ π π = πππ π 90π b. Using πΌ = π βΆ 30Ω = ππ¨ c. Using π = πΌπ βΆ (3π΄)(5Ω) = πππ½ 3. a. Using π π = π 1 + π 2 βΆ 5Ω + 10Ω = 15Ω βΆ π π = πππ 1 π 45π b. Using πΌ = π βΆ 15Ω = ππ¨ c. Using π = πΌπ βΆ (3π΄)(15Ω) = πππ½ 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 a. Using π = π + π + π … βΆ π 1 2 3 1 π π 1 1 1 = 15Ω + 15Ω + 15Ω βΆ 1 π π 3 = 15Ω βΆ πΉπ» = ππ b. Using πΌπ = πΌ1 + πΌ2 + πΌ3 … ππ ππ ππ 30.0π 30.0π 30.0π πΌπ = ( ) + ( ) + ( ) = ( )+( )+( ) : π°π» = ππ¨ π 1 π 2 π 3 15Ω 15Ω 15Ω π c. Using πΌ = π βΆ πΌ = 2. 1 1 30.0π βΆ π° = ππ¨ 15Ω 1 1 a. Using π = π + π + π … βΆ π 1 2 3 1 π π 1 1 3 = 12Ω + 15Ω = 20Ω βΆ πΉπ» = π. πππ b. Using πΌπ = πΌ1 + πΌ2 + πΌ3 … ππ ππ ππ 30.0π 30.0π πΌπ = ( ) + ( ) + ( ) = ( )+( ) : π°π» = π. ππ¨ π 1 π 2 π 3 12Ω 15Ω 2 π c. Using πΌ = π 30.0π βΆ π°π = π. ππ¨ 12Ω 30.0π πΌ2 = βΆ π°π = ππ¨ 15Ω πΌ1 = 3. 1 1 1 1 a. Using π = π + π + π … βΆ π 1 2 3 1 π π 1 1 1 = 120.0Ω + 60.0Ω + 40Ω βΆ 1 π π 1 = 20Ω βΆ πΉπ» = πππ b. Using πΌπ = πΌ1 + πΌ2 + πΌ3 … ππ ππ ππ 12.0π 12.0π 12.0π πΌπ = ( ) + ( ) + ( ) = ( )+( )+( ) : π°π» =. ππ¨ π 1 π 2 π 3 120Ω 60Ω 40Ω π c. Using πΌ = π βΆ 12.0π βΆ π°π =. ππ¨ 120Ω 12.0π πΌ2 = βΆ π°π =. ππ¨ 60Ω 12.0π πΌ3 = βΆ π°π =. ππ¨ 40Ω πΌ1 = 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 π = 60Ω + 60Ω = 30Ω βΆ πΉπ π = πππ 23 c. Using π π = π 1 + π 2 3 = 30Ω + 30Ω βΆ πΉπ» = πππ π d. Using πΌπ = π π = π 60π 120.π 60Ω βΆ π°π» = ππ¨ e. Voltage drop across the 30 Ohm resistor = (30Ω)(2π΄) = πππ½ f. Voltage drop across parallel portion = 120π − (ππππ πππππ π π πππππ ππππ‘πππ) = π g. Current through each resistor may be found using πΌ = π : πππ½ π°π = πππ = ππ¨ (same as total current, as it should be) πππ½ π°π = πππ = ππ¨ πππ½ π°π = πππ = ππ¨ 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 π = π + π + π = 15Ω + 15Ω + 15Ω = 5Ω βΆ πΉπ»ππππππππ = ππ πππππππππ 1 2 3 Using the series resistance formula with the 10Ohm resistor and the equivalent parallel resistance of 5Ohms: π π = π 1 + π 2 βΆ 10Ω + 5Ω = 15Ω The equivalent resistance for the entire circuit is πππ. 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
