At room temperature (27.0 °C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 117 Ω, given that the temperature coefficient of the material of the resistor is \(1.70 \times 10^{-4} °C^{-1}.\)
At room temperature (27.0 °C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 117 Ω, given that the temperature coefficient of the material of the resistor is \(1.70 \times 10^{-4} °C^{-1}.\)
Solution and Explanation
Room temperature, T = 27 °C
Resistance of the heating element at T, R = 100 Ω
Let \(T_1\) is the increased temperature of the filament.
Resistance of the heating element at \(T_1, R_1 = 117 Ω \)
Temperature co-efficient of the material of the filament,
\(α = 1.70\times 10^{-4} \degree C^{-1}\)
α is given by the relation,
\(α = \frac{R_1-R}{R(T_1-T)}\)
\(T_1-T =\frac{ R_1-R}{Rα}\)
\(T_1-27 = \frac{117 - 100}{100( 1.70\times10^{-4})}\)
\(T_1-27 = 1000\)
\(T_1 = 1027 °C\)
Therefore, at 1027°C, the resistance of the element is 117Ω.
Top Questions on Current electricity
- The equivalent resistance between points A and B in a circuit with two resistors of 6 \(\Omega\) each connected in parallel is:
- BITSAT - 2025
- Physics
- Current electricity
- The above battery sends a current \( I_1 \) when \( R = R_1 \) and a current \( I_2 \) when \( R = R_2 \). Obtain the internal resistance of the battery in terms of \( I_1 \), \( I_2 \), \( R_1 \), and \( R_2 \).
- CBSE CLASS XII - 2025
- Physics
- Current electricity
- Three wires A, B, and C of the same material have lengths and area of cross-sections as \( (2l, \frac{A}{2}) \), \( (l, A) \) and \( (\frac{l}{2}, 2A) \), respectively. If the resistances of these wires are \( R_A, R_B, R_C \) respectively, then:
- CBSE CLASS XII - 2025
- Physics
- Current electricity
- A battery of emf E and internal resistance r is connected to an external resistance R.
(I) Expression for current I and maximum current:.
(II) Terminal voltage V and its maximum value:.- CBSE CLASS XII - 2025
- Physics
- Current electricity
- Expression for internal resistance in terms of I1, I2, R1, R2:
- CBSE CLASS XII - 2025
- Physics
- Current electricity
Questions Asked in CBSE CLASS XII exam
- Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.
- CBSE CLASS XII - 2025
- Functions
- Agro-startups and rural enterprises are becoming increasingly vital for rural development in India. They address the critical challenges faced by rural sector in India. These ventures bring in technological innovations such as precision farming, IT-based monitoring system and data-driven decision making tools that enhance productivity and resource efficiency. By streamlining supply chains and creating direct market linkages, they ensure better pricing for farmers and reduce dependency on traditional intermediaries. Such enterprises contribute actively to employment generation in the rural areas. The government has demonstrated a continuous policy and financial support for agri-startups and entrepreneurs through various programs like RKVY-RAFTAAR, the Agri- infrastructure fund and Agri-SURE.
On the basis of given text and common understanding, answer the following questions:- CBSE CLASS XII - 2025
- Rural Development
Read the following text carefully:
Union Food and Consumer Affairs Minister said that the Central Government has taken many proactive steps in the past few years to control retail prices of food items. He said that the government aims to keep inflation under control without compromising the country’s economic growth. Retail inflation inched up to a three-month high of 5.55% in November 2023 driven by higher food prices. Inflation has been declining since August 2023, when it touched 6.83%. 140 new price monitoring centres had been set up by the Central Government to keep a close watch on wholesale and retail prices of essential commodities. The Government has banned the export of many food items like wheat, broken rice, non-basmati white rice, onions etc. It has also reduced import duties on edible oils and pulses to boost domestic supply and control price rise. On the basis of the given text and common understanding,
answer the following questions:- CBSE CLASS XII - 2025
- Government Budget and the Economy
- Distinguish between Physical Capital and Human Capital.
- CBSE CLASS XII - 2025
- Human Capital Formation
- “In the recent Budget the Government allocated funds for construction of new metro lines in smart cities to improve public transportation and reduce pollution.”
Identify the nature of government expenditure \& its objective.- CBSE CLASS XII - 2025
- Government Budget and the Economy
Concepts Used:
Temperature Dependence of Resistance
The temperature dependence of resistance is a fundamental property of all materials that conduct electricity. Generally, the resistance of a conductor increases with an increase in temperature. This phenomenon is known as a positive temperature coefficient of resistance.
The reason for this temperature dependence of resistance is related to the interaction of electrons with the crystal lattice of the material. At lower temperatures, the lattice vibrations are minimal, and the electrons are free to move through the material with minimal scattering. This results in a low resistance to the flow of current. However, as the temperature increases, the lattice vibrations increase, causing the electrons to scatter more frequently, which increases resistance.
This phenomenon is governed by the relationship between resistance and temperature known as the temperature coefficient of resistance. The temperature coefficient of resistance is defined as the rate at which resistance changes with respect to temperature. The temperature coefficient of resistance is positive for most metals and semiconductors, meaning that resistance increases with increasing temperature.
However, there are a few materials, such as carbon and certain semiconductors, which exhibit a negative temperature coefficient of resistance. In these materials, the resistance decreases as the temperature increases.
The temperature dependence of resistance has important practical implications in the design and operation of electrical circuits and devices. For example, it is essential to consider the effect of temperature on the resistance of electronic components to ensure reliable and efficient operation of devices over a range of temperatures.