1. Solving series circuit problems

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1 Name: Skill Sheet 20. Parallel and Series Circuits There are two major types of electrical circuits: series and parallel. In a series circuit, current follows only one path. In a parallel circuit, the current has two or more possible paths. In both types of circuits, the current travels from the positive end of the battery toward the negative end. The amount of energy used by a circuit (series or parallel) must equal the energy supplied by the battery. In this way, electrical circuits follow the law of conservation of energy. Understanding these facts will help you solve problems that deal with series and parallel circuits.. Solving series circuit problems Now it is time for you to test your knowledge of series and parallel circuits by answering the questions below. You will have to use Ohm s law to solve many of the problems, so remember: Voltage (volts) Current (amps) = Resistance (ohms) Some questions ask you to calculate a voltage drop. We often say that each resistor creates a separate voltage drop. As current flows along a series circuit, each resistor uses up some energy. As a result, the voltage gets lower after each resistor. If you know the current in the circuit and the resistance of a particular resistor, you can calculate the voltage drop using Ohm s law. Voltage drop (volts) = Current (amps) Resistance of one resistor (ohms). Use the series circuit pictured at right to answer questions a-e below. a. What is the total voltage of the circuit? b. What is the total resistance of the circuit? c. What is the current flowing through the circuit? d. What is the voltage drop across each light bulb? (Remember that voltage drop is calculated by multiplying current in the circuit by the resistance of a particular resistor: V = IR.) e. Draw the path of the current flow on the diagram.

2 Skill Sheet 20. Parallel and Series Circuits 2. Use the series circuit pictured at right to answer questions a-c below. Consider each resistor equal to all others. a. What is the resistance of each resistor? b. What is the voltage drop across each resistor? c. On the diagram, show the amount of voltage in the circuit before and after each resistor. 3. Use the series circuit pictured at right to answer questions a-d below. a. What is the resistance of the circuit? b. What is the current flowing through the circuit? c. What is the voltage drop across each resistor? d. On the diagram, show the amount of voltage in the circuit before and after each resistor. 2. Solving parallel circuit problems A parallel circuit has at least one point where the circuit divides, creating more than one path for current. Each path is called a branch. The current through a branch is called branch current. Remember that if current flows into a branch in a circuit, the same amount of current must flow out again. This rule is known as Kirchhoff s current law. For example, suppose you have three light bulbs connected in parallel, and each has a current of amp. The battery must supply 3 amps since each bulb draws amp. Before the first branch point, 3 amps are flowing. One amp goes down the first branch to the first bulb, and 2 amps flow on to supply the next two bulbs. 2

3 Skill Sheet 20. Parallel and Series Circuits. Use the parallel circuit pictured at right to answer questions a-c below. a. What is the total voltage for the circuit? b. What is the current flow through each branch? c. What is the voltage in each branch? 2. Compare the circuits in Part, question and Part 2, question. What is the current flow through each bulb in the series circuit compared with the current flow through each bulb in the parallel circuit? Which bulbs would be brighter? Explain your reasoning. 3. Use the parallel circuit pictured at right to answer questions a-d below. a. What is the voltage through each branch? b. What is the current flow through each branch? c. What is the power of each resistor? (Remember that power is current multiplied by voltage.) d. What is the relationship between current and power? 3

4 Name: Skill Sheet 20.2 Network Circuits Network circuits are combinations of series and parallel circuits. Therefore, solving problems that involve networks circuits require using one or two formulas. In this skill sheet, you will practice solving these kinds of problems.. The formulas for solving network circuit problems When solving resistor network circuits we have to remember the following formulas:. Ohm s law: V = IR 2. Combining resistors: R total equals total resistance for the circuit: a. In series: R total = R + R b. In parallel: R total = R R 2 3. Kirchhoff s voltage law: The sum of voltages around a loop is zero. 4. Kirchhoff s current law: The sum of currents into a node equals the sum of currents out of the node. Example problem: For the following circuit, calculate the total resistance and the total current drawn from the 6-volt battery. First notice that resistors R 5 and R 6 are in parallel and that they combine to give a resulting resistance of.5 ohms. Next, notice that resistors R 3 and R 4 are in series resulting in a resistance of 2 ohms. The resulting 2 ohms resistance is connected in parallel with another 2-ohm resistor. Thus the combined resistance of R 3, R 4, and R 2 is ohm. Now the circuit looks like: We see now that the -ohm resistors are connected in series. Therefore, they represent a 2-ohm resistor connected in parallel with the.5-ohm resistor. The 2-ohm resistor in parallel with the.5 ohm gives a total resistance of 6 7 or 0.86 ohms. The total current drawn from the battery can be now found by applying Ohm s law: I = V -- = volts = 7 A R 6/7Ω

5 Skill Sheet 20.2 Network Circuits 2. Problems. A 2-volt battery is connected to the resistor network shown on the schematic. Calculate the current through each resistor in the network. 2. Combine resistances and calculate the total resistance. 3. Calculate the total current drawn from the 9-volt battery. 4. For the circuit at right, trace the path of the current through the circuit and then answer the following questions: a. Does current flow through R5? Why or why not? b. Given your answer to (a), what is the total resistance for the circuit? c. Given your answer to (a), what is the total current leaving the battery? d. What is the current through resistor R 3? e. What is the voltage across R 5? Explain your answer. 2

6 Skill Sheet 20.2 Network Circuits 5. Find the total current drawn from the 6-volt battery. What is the voltage across resistor R 4? 6. What is the voltage across the 5-ohm resistor? 7. Calculate the voltage across points A and B (V AB ) when the resistor R 4 is 0 Ω. HINT: Find the voltage at A (V A ) and the voltage at B (V B ) and subtract. 3