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Questions and Answers
A wire's resistance is found to increase. Which of the following adjustments would independently reduce the resistance back to its original value?
A wire's resistance is found to increase. Which of the following adjustments would independently reduce the resistance back to its original value?
- Decreasing the wire's length, while maintaining a constant temperature. (correct)
- Increasing the wire's cross-sectional area, while decreasing the temperature for a semiconductor.
- Decreasing the wire's cross-sectional area, while maintaining a constant temperature.
- Increasing the wire's length, while also increasing the temperature.
Two wires, one silver and one copper, have the same length and cross-sectional area. If both wires are subjected to the same voltage, which wire will exhibit a greater current flow, and why?
Two wires, one silver and one copper, have the same length and cross-sectional area. If both wires are subjected to the same voltage, which wire will exhibit a greater current flow, and why?
- The silver wire, because silver has a lower resistivity than copper, allowing for greater current flow. (correct)
- Both wires will exhibit the same current flow, as the voltage applied is the same for both.
- The copper wire, because copper has a lower temperature co-efficient.
- The copper wire, because copper is a more common conductor and thus carries current more effectively.
A metallic wire's resistance is measured at two different temperatures. At $20°C$, its resistance is $R_1$, and at $50°C$, its resistance is $R_2$. How does $R_2$ compare to $R_1$, and what property of metals explains this change?
A metallic wire's resistance is measured at two different temperatures. At $20°C$, its resistance is $R_1$, and at $50°C$, its resistance is $R_2$. How does $R_2$ compare to $R_1$, and what property of metals explains this change?
- $R_2 < R_1$ because metals have a negative temperature coefficient.
- $R_2 > R_1$ because metals have a positive temperature coefficient. (correct)
- $R_2 \approx R_1$ because the temperature change is relatively small.
- $R_2 = R_1$ because the temperature change does not affect the resistance of metals.
In a digital thermometer that utilizes a metal resistor to measure temperature, an increase in temperature leads to:
In a digital thermometer that utilizes a metal resistor to measure temperature, an increase in temperature leads to:
A copper wire has a resistance of $0.1\ \Omega$ at $20°C$. The temperature coefficient of resistance for copper is $0.00393\ /^\circ C$. If the temperature of the wire increases to $70°C$, what is the approximate new resistance of the wire?
A copper wire has a resistance of $0.1\ \Omega$ at $20°C$. The temperature coefficient of resistance for copper is $0.00393\ /^\circ C$. If the temperature of the wire increases to $70°C$, what is the approximate new resistance of the wire?
A semiconductor material is used in a circuit. If the temperature of the semiconductor increases, what happens to its resistivity and conductivity?
A semiconductor material is used in a circuit. If the temperature of the semiconductor increases, what happens to its resistivity and conductivity?
A nichrome wire is used as a heating element. Which change to the wire would decrease the amount of heat it produces, assuming constant voltage?
A nichrome wire is used as a heating element. Which change to the wire would decrease the amount of heat it produces, assuming constant voltage?
Suppose a wire connected to a power source experiences a decrease in current flow. Assuming the voltage remains constant, what does this indicate about the wire's resistance and potentially its temperature, if it is made of metal?
Suppose a wire connected to a power source experiences a decrease in current flow. Assuming the voltage remains constant, what does this indicate about the wire's resistance and potentially its temperature, if it is made of metal?
A 20 m long wire with a radius of 4 mm carries a current of 0.5 A. The voltage drop across the wire is measured to be 0.1 V. What is the approximate resistivity of the wire's material?
A 20 m long wire with a radius of 4 mm carries a current of 0.5 A. The voltage drop across the wire is measured to be 0.1 V. What is the approximate resistivity of the wire's material?
A circuit contains a component made of silicon. Under what circumstances would increasing the temperature improve the performance (conductivity) of this component?
A circuit contains a component made of silicon. Under what circumstances would increasing the temperature improve the performance (conductivity) of this component?
Flashcards
Resistivity (ρ)
Resistivity (ρ)
Opposition to electric current flow in a material.
Material Resistivity - Metals
Material Resistivity - Metals
Metals have resistivity around 10^-8, good conductors.
Material Resistivity - Insulators
Material Resistivity - Insulators
Very high resistivity, do not conduct electricity.
Metals and Temperature
Metals and Temperature
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Semiconductors and Temperature
Semiconductors and Temperature
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Positive Temperature Coefficient (α)
Positive Temperature Coefficient (α)
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Negative Temperature Coefficient (α)
Negative Temperature Coefficient (α)
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Resistance Thermometry
Resistance Thermometry
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Voltage Drop Calculation
Voltage Drop Calculation
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Current Change Implies Temp Change
Current Change Implies Temp Change
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Study Notes
Resistance of a Wire
- Resistance (R) = Resistivity (ρ) × Length (L) / Area (A)
- Longer wires possess greater resistance because resistance is directly proportional to length.
- Thin wires have higher resistance than thicker wires of the same length, as resistance is inversely proportional to the cross-sectional area.
- Thick wires exhibit less resistance with more space available for electron movement and higher current flow, similar to a multi-lane highway.
Resistivity (ρ)
- Resistivity indicates a material's ability to oppose electric current.
- Good conductors (metals) have low resistivity values, typically around 10^-8.
- Silver has a resistivity of 1.59 × 10^-8, while copper's resistivity is approximately 1.68 × 10^-8.
- Silver is a better conductor than copper due to its lower resistivity.
Material Resistivity
- Metals: Resistivity is around 10^-8; they make good electrical conductors.
- Semiconductors: Have higher resistivity values and conduct electricity moderately well; useful for resistors.
- Carbon graphite: Resistivity ranges from 3 to 60 × 10^-5.
- Germanium: Resistivity is around 10^-3.
- Silicon: Resistivity ranges from 10^-1 to 10^1; it's generally not a good conductor.
- Insulators: Have very high resistivity (e.g., glass from 10^9 to 10^12) and do not conduct electricity.
Resistivity as a Function of Temperature
- ρ_T = ρ_0 [1 + α(T - T_0)] can determine resistivity at a specific temperature.
- Metals: Resistivity increases as temperature increases (positive temperature coefficient).
- Increased temperature in metals results in more frequent electron collisions, which reduces drift velocity and increases resistance.
- Metals conduct electricity more effectively at low temperatures.
- Some metals become superconductors at very low temperatures, exhibiting virtually no resistance.
- Semiconductors: Resistivity decreases, and conductivity improves as temperature increases (negative temperature coefficient).
Temperature Coefficient (α)
- Metals: Exhibit a positive temperature coefficient, demonstrating a direct relationship between temperature and resistivity.
- Semiconductors: Exhibit a negative temperature coefficient, indicating an inverse relationship between temperature and resistivity.
Measuring Temperature Using Resistance
- Digital thermometers use the principle that resistance changes with temperature to measure temperature.
- R_T = R_0 [1 + α(T - T_0)] allows for temperature calculation based on resistance, assuming constant length and area.
- Temperature can be calculated by knowing a metal's resistance at one temperature and then measuring its resistance at another temperature.
Calculation Example: Copper Wire Resistance
- A 15 m long copper wire with a 3 mm radius has a resistivity of 1.68 × 10^-8 at 20°C and a temperature coefficient of 0.0068.
- R = ρ × L / A is used to calculate resistance at 20°C.
- Convert the radius to meters first: 3 mm = 3 × 10^-3 m.
- Area calculation: A = π × (3 × 10^-3)^2.
- Finding the resistance: R = (1.68 × 10^-8 × 15) / (π × (3 × 10^-3)^2) = 0.008913 ohms.
Temperature Effect on Resistance
- To calculate the new resistance at 50°C, R = R_0 [1 + α(T - T_0)] should be used.
- Given R_0 = 0.008913 ohms, α = 0.0068, T = 50°C, and T_0 = 20°C.
- Result: R = 0.008913 [1 + 0.0068(50 - 20)] = 0.01073 ohms.
- Increasing temperature from 20°C to 50°C causes increased resistance.
- Increasing temperature increases the resistivity of metals and thus increases resistance.
Voltage Drop Calculation
- With a 200 milliamp (0.2 A) current through the wire at 20°C, voltage drop V = I × R.
- V = 0.2 A × 0.008913 ohms = 0.0017826 volts, or 1.783 millivolts.
- The voltage drop per meter is 1.783 millivolts / 15 m = 0.119 millivolts per meter.
- A 300 m wire would have a voltage drop of 0.119 millivolts/m × 300 m = 35.7 millivolts.
Determining Temperature Change from Current
- Given connectivity to a 12V battery and a current of 0.45A at 20°C, a modification in current shows a modification in temperature.
- A new temperature must be calculated if the current decreases to 0.41 amps.
- Reduced current indicates increased resistance; in metals, this occurs with increased temperature.
Calculating New Temperature
- Resistance calculation at 20°C: R = 12V / 0.45A = 26.667 ohms.
- Resistance calculation at the new temperature: 12V / 0.41A = 29.268 ohms.
- R_T = R_0 [1 + α(T - T_0)] is used to solve for the new temperature T.
- 29.268 = 26.667 [1 + 0.0068(T - 20)] results in T = 34.34°C.
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Description
Understand wire resistance and resistivity. Resistance is directly proportional to length and inversely proportional to cross-sectional area. Good conductors have low resistivity, with silver being a better conductor than copper.
