Resistance 7a Flashcards
What is resistance in the context of electricity?
Resistance is an electrical property of a conductor that determines how much current flows for a given voltage.
What is the relationship between current, resistance, and voltage in a conductor?
For a given current, a higher resistance requires a higher voltage to be applied across the conductor.
What factors determine the numerical value of a conductor’s resistance?
The resistance of a conductor depends on the material from which it is made, its shape, and its size.
How does the length of a resistor affect its resistance?
Resistance increases in direct proportion to the length of a resistor; if the material is doubled in length, the resistance is also doubled.
How does the cross-sectional area of a resistor affect its resistance?
Resistance increases in inverse proportion to the cross-sectional area of a resistor; if the resistor is doubled in cross-sectional area, the resistance is halved.
Why is it important to compare samples of different materials with the same dimensions?
Comparing samples with the same dimensions ensures a fair comparison of the resistances of various materials.
How do all materials relate to the flow of electric current?
All materials oppose the flow of an electric current to some extent.
What happens to the resistance if the length of a conductor is doubled?
If the length of a conductor is doubled, its resistance also doubles.
What happens to the resistance if the cross-sectional area of a conductor is doubled?
If the cross-sectional area of a conductor is doubled, its resistance is halved.
What should be done to fairly compare the resistances of different materials?
To fairly compare the resistances of different materials, samples should be prepared with the same dimensions.
What is the effect of the material on the resistance of a conductor?
The material from which a conductor is made significantly affects its resistance.
Why does resistance increase with length and decrease with cross-sectional area?
Resistance increases with length because the electrons encounter more collisions over a longer path. It decreases with cross-sectional area because a larger area allows more paths for the electrons to flow through, reducing collisions.
Q: How is the relationship between length, cross-sectional area, and resistance mathematically expressed?
R=ρ x L/A
What does the symbol 𝜌 represent in the resistance formula?
The symbol
𝜌
ρ represents the specific resistance or resistivity.
What are the units of specific resistance (resistivity)?
The units of specific resistance (resistivity) are ohm metres (Ωm).
How should the cross-sectional area be measured when using the formula for specific resistance?
The cross-sectional area should be measured in square metres (m²) when using ohm metres (Ωm), or in square millimetres (mm²) when using ohm millimetres squared per metre (Ωmm²/m).
What are fixed resistors and variable resistors?
Fixed resistors are designed to provide a constant value of resistance, while variable resistors are designed to provide a range of resistance values.
How do you calculate the resistance of a wire made from a material with a given specific resistance?
Use the formula
𝑅=𝜌𝐿/𝐴
ensuring the units of specific resistance and cross-sectional area are compatible.
What is the resistance of a 10 m copper wire with a cross-sectional area of 2 mm² and a specific resistance of 0.020 Ωmm²/m?
R= 0.020×10/2 = 0.1Ω
What is the resistance of a 10 m iron wire with a cross-sectional area of 2 mm² and a specific resistance of 0.100 Ωmm²/m?
𝑅=0.100×10/2 = 0.5Ω
What is the resistance of a copper wire that is 1 m long with a cross-sectional area of 1 mm² at 20 °C?
0.0178 Ω
How does doubling the length of a copper wire affect its resistance, if the cross-sectional area remains the same?
Doubling the length of a copper wire doubles its resistance.
What is the resistivity of silver at 20 °C?
The resistivity of silver at 20 °C is 0.016 Ωmm²/m.
What is the resistivity range of iron at 20 °C?
The resistivity range of iron at 20 °C is 0.10 to 0.15 Ωmm²/m.
Why might engineering often quote specific resistance in ohm millimetres squared per metre (Ωmm²/m)?
Ohm millimetres squared per metre (Ωmm²/m) is easier to relate to a standard piece of wire with dimensions of 1 m in length and 1 mm² in cross-sectional area.
What happens to the resistance of a copper wire three times as long as a 1 m wire, with the same cross-sectional area?
The resistance of a copper wire three times as long will be three times the resistance of a 1 m wire.
List the resistivity of copper, aluminium, and gold at 20 °C.
Copper: 0.01786 Ωmm²/m
Aluminium: 0.02857 Ωmm²/m
Gold: 0.023 Ωmm²/m**
What must be considered when using the formula for calculating resistance with specific resistance?
Ensure the units of specific resistance are compatible with the units of the cross-sectional area being used.
How do you calculate the total resistance of a group of resistors?
The method depends on how the resistors are connected. Use different formulas for series and parallel connections.
What happens to the current in resistors connected in series?
The current flows through all resistors in turn and has the same value for each resistor.
How do you calculate the total resistance for resistors in series?
Add the values of the resistors together.
𝑅 Total=𝑅1+𝑅2+𝑅3+…
What are the three typical features of a series connection?
The voltage is divided between the resistors.
The current is the same through all components.
The individual resistances are added together to find the total resistance.**
What is a potential divider (or voltage divider)?
A series connection where each resistor has only a part of the total voltage across it. The output voltage can be tapped at a certain point called the “pick-up.”
What happens to the current in resistors connected in parallel?
The current splits up, and a smaller current flows through each available path.
How do you calculate the total resistance for resistors in parallel?
Add the reciprocals of the individual resistances to find the reciprocal of the total resistance.
1/𝑅Total=1/𝑅1+1/𝑅2+1/𝑅3 + …
What are the three typical features of a parallel connection?
Voltage is the same across each resistor.
The total current is the sum of the currents in each branch.
The total resistance is lower than the lowest individual resistance.**
How does the area through which the current can flow change in a parallel connection?
The area increases, which decreases the resistance.
How is the total voltage in a series circuit related to the individual voltages across each resistor?
The total voltage is the sum of the voltages across each resistor.
𝑉 Total=V1+𝑉2+𝑉3+…
In a series circuit, how is the voltage across each resistor related to its resistance?
The voltage across each resistor is proportional to its resistance.
How do you describe the current in a parallel circuit using Kirchhoff’s first law?
The total current is the sum of the currents in each branch.
What effect does adding more resistors in parallel have on the total resistance?
Adding more resistors in parallel decreases the total resistance.
What happens to the voltage across resistors in parallel?
The voltage across each resistor is the same.
What analogy can describe the current flow in a series circuit?
Current in a series circuit is like water flowing through different sections of the same hose pipe.
How do you determine the total resistance for a combination of series and parallel resistor networks?
Apply the series and parallel formulas in turn, step by step.
What law can be used to show the relationship between the total and individual resistances in parallel?
Kirchhoff’s first law and Ohm’s law.
What is the formula for the total resistance
𝑅Total in a parallel circuit with resistors
𝑅1,𝑅2,…,𝑅𝑛?
1/R Total=1/R1+1/R2+…+ 1/Rn
how do you calculate the resistance of a circuit with both parallel and series resistors?
first calculate parallel resistors so as to turn it into a series resistance then calculate the series resistors
What is a variable resistor?
An electro-mechanical transducer that has adjustable resistance values, usually working by sliding a contact (wiper) over a resistive element.
What is a potentiometer?
A three-terminal variable resistor used to control voltage.
What is a rheostat?
A two-terminal variable resistor used to control current.
How is a potentiometer connected?
Terminal 3 is connected to the input voltage, terminal 1 to the ground, and terminal 2 is the variable output voltage.
What is the function of a potentiometer?
To control voltage by acting as an adjustable voltage divider, commonly used in volume controls and lighting circuits.
How is a rheostat connected?
Option 1: Terminal 3 is connected to the input current, and terminal 2 provides the output current, with terminal 1 not connected. Option 2: Terminal 3 is connected to the input current, and terminals 1 and 2 form the output terminal.
What is the difference between a potentiometer and a rheostat?
The difference lies in their connections and applications: potentiometers control voltage with three terminals, while rheostats control current with two terminals.
What is a digital potentiometer?
An electronically controlled variable resistor.
What are some types of variable resistors other than mechanically varied resistors?
Positive or negative temperature coefficient resistors and voltage-dependent resistors.
What is a pre-set potentiometer?
A potentiometer mounted on printed circuit boards, with a limited range, usually set during manufacture or maintenance.
What is a pre-set rheostat?
A rheostat mounted on printed circuit boards, with a limited range, usually set during manufacture or maintenance.
How does a potentiometer vary the speed of DC motors?
By adjusting the voltage supplied across the motor, which changes the motor’s speed.
What is the purpose of a rheostat in an electric circuit?
To restrict the current by increasing the resistance in the circuit.
How is the resistance in a potentiometer adjusted?
The position of the wiper determines the resistance ratio, forming a potential divider and controlling the voltage.
How is the resistance in a rheostat adjusted?
The position of the wiper determines the resistance between the terminals, which adjusts the current in the circuit.
What symbol represents a potentiometer in circuit diagrams?
What symbol represents a rheostat in circuit diagrams?
In which devices are potentiometers commonly used?
Volume controls in audio circuits and brightness controls in lighting circuits.
In which devices are rheostats commonly used?
Circuits where current needs to be controlled or restricted.
How does a pre-set rheostat function?
It allows for adjustment of the resistance, set during manufacture or maintenance, to control current in the circuit.
