I. Resistance and Resistivity
In our overview of circuits, we defined resistance as any opposition to the flow of charges. Resistance tells us how well an object stops electron flow. This is important because electron flow must be managed in some circuits. We use resistors to manage the flow of electrons.
Resistivity is an intrinsic property of a material. Itโs a property that is dependent on the nature of the material itself. Ceramics have high resistivity, which makes it a good material for resistors. In contrast, copper has a low resistivity, which makes it a good material for wires due to its high conductivity. We can relate resistance and resistivity using the equation.
Resistors work by impeding the flow of current. They help manage the flow of electrons by creating a narrow path for electrons to travel to, which also turns electrical energy into heat. Since resistors impede electron flow, a voltage drop occurs when a resistor is placed in a circuit. Referring to the image on the right, we can see two resistors. The battery has a voltage of 30 V, and a current of 3A runs across the circuit.
Letโs take a look at how resistors cause a voltage drop by observing the following calculations:
Resistor 1:
Resistor 2:
As you can see, the voltage across the two resistors changed. From having a voltage of 30V coming from the battery, the voltage is reduced to 18 V upon reaching the first resistor. Through the second resistor, the voltage is further reduced to 12 V. Resistors work by reducing the voltage across the circuit.
If you notice, the sum of voltages 1 and 2 equals the total voltage released by the battery. This is known as Kirchhoff's Voltage Law, which states that the sum of all the voltage drops in a closed circuit must equal to zero. Considering our example, Kirchoffโs law should look like this:
II. Parallel and Series Circuit
Circuits can be organized in two ways: series and parallel.
A. Series
In a series circuit, the current travels through a single path. Components in this type of circuit are also connected from end to end in one line. As we add more bulbs or resistors across the circuit, the light becomes significantly dimmer because of the voltage drop across each bulb. A load such as a bulb acts like a resistor since it impedes electron flow to light up. Since the current travels in a single path, the current each component receives is the same throughout the circuit. When one component fails, such as Bulb 2, the path of electron flow becomes disrupted, affecting the flow of other bulbs. The total voltage and resistance across a series circuit can be calculated by getting the sum of the individual voltage and resistance. Hereโs a summary of how voltage, current, and resistance varies across a series circuit.
B. Parallel
Parallel circuits have their components parallel to each other. Each load/resistor is connected in parallel to the other components. Because of this, each load receives the same voltage. Current may vary across each line. For example, the current in R1 may not be equal to the current in R2. If we look back at Ohmโs law, our resistance and current will vary if we hold the voltage constant. The direction of the current flow also varies through each branch. Electrons can flow in different directions, going straight or moving to another branch where a load is present. Because of the nature of electron flow, the other loads are unaffected when one component fails. If bulb 2 breaks down, the path for electrons will still be undisrupted since there are multiple paths for electrons to travel to. We calculate the voltage, current, and resistance differently for parallel circuits.
III. Conclusion
Resistance is an important topic in circuits. Household appliances typically use resistors to manage current flow and avoid overloading. Resistors manage the current flow by reducing the โpressureโ of electron flow. They are usually made of materials with high resistivity. Circuits can be connected in series and parallel. Series circuits are connected in one line with only one path for electron flow. In contrast, parallel circuits are connected parallel to each other, creating many paths for electrons to flow into. Both circuits have different ways to calculate the voltage, resistance, and current due to the different nature of electron flow.
IV. Key Terms
- Parallel Circuit - A circuit with components arranged parallel to each other.
- Series Circuit - A circuit with components arranged to form a single path.
- Resistance - A measure of how well a material resists electron flow.
- Resistivity - An intrinsic property of a material that describes how well a material resists electric current.
- Resistor - A component that impedes electron flow.
V. Practice Questions
Sample Practice Question 1
Which type of circuit is preferable for households with multiple bulbs?
A. Series circuits because the power source can deliver power more efficiently.
B. Series circuit because the flow of electrons has one straight path.
C. Parallel circuit because electron flow is not restricted to one path.
D. Parallel circuits are used because the power distribution is more efficient.
Ans. C
Sample Practice Question 2
A circuit has a resistor with a resistance of 2ฮฉ in series followed by 2 resistors in parallel, each with a resistance of 3ฮฉ. Calculate the total resistance.
A.
B.
C. 8ฮฉ
D.
Ans. A
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