**Title: Understanding Resistance and Temperature Effects in Tungsten Filaments****Introduction to Resistive Heating in Conductors**Resistive conductors tend to heat up when current flows through them. The temperature of the conductor typically depends on the amount of current it carries; a higher current leads to a higher temperature. Additionally, the resistivity of a metallic conductor increases with increasing temperature. Therefore, the resistance of a piece of metal generally increases if the current in the metal increases. This effect is usually negligible if the temperature of a circuit element does not vary too much during its operation. However, this effect can be significant in circuit elements that experience large temperature variations, like incandescent light bulbs and the heating elements in a toaster.**Incandescent Light Bulbs and Tungsten Filaments**The main component in an incandescent light bulb is a coiled filament of tungsten that is 580 mm long with a diameter of 46 μm. At 20°C, tungsten has a resistivity of \(5.25 \times 10^{-8} \, \Omega \cdot m\). Its temperature coefficient of resistivity is \(0.0045 \, (\text{°C})^{-1}\), and this remains accurate even at high temperatures.**Problem Set**(a) **Initial Temperature Conditions:** - Initially, the temperature of the filament is 20°C and there is no current flowing through it. What is the resistance of the light bulb under these conditions?(b) **Effect of Applied Voltage:** - If a voltage is applied across the terminals of the light bulb, current begins to flow through it. The temperature \(T\) of the filament increases linearly with the current \(I\) through it, according to the equation \( T(I) = (2500^\circ C \cdot A^{-1})I + 20^\circ C\). What is the current through the light bulb when the voltage across its terminals is 120 V? - (Hint: Use the equation given in this part to determine the resistance of the light bulb as a function of current. Substitute that result into the equation \(V = IR\), and solve for the current \(I\).)(c) **Temperature at Applied Voltage:** - What is the temperature of the filament when the voltage across it is 120 V?(d) **Resistance at Applied Voltage:** - What is the resistance of the light bulb when the voltage across

Given that, Length of Conductor (L)=580 mm. Radius of Conductor (r)=23 μm. Resistivity of Conductor (ρ)=5.25*10-8 Ωm. Temperature Coefficient (α)= 0.0045 ∘C-1 Here we have to find out the resistance of wire at some temperature, Current through the wire, & temperature.a. Let resistance of wire be R, Cross section area of wire be A. As we know that R=ρLAΩ =(5.25*10-8)*(580*10-3)π*(23*10-6)2Ω=5.25*580*1023*23*πΩ=18.33 Ω Hence, the resistance of wire will be 18.33Ωb. We have, R=18.33Ω T(I)=(2500∘C A-1)I +20∘C V (Potential Difference)=120 V As per Ohm's Law, I=VR =12018.33A =6.55 A Hence, the current through the light bulb will be 6.55 A.c. According to the question, T(I)=(2500∘C A-1)I +20∘C We have, I=6.55A then, T(6.55A)=(2500∘C A-1)(6.55A) +20∘CT(6.55A)=(16375)∘C+20∘C =16385∘C Hence, Temperature of filament when voltage across it is 120V,is 16385∘Cd. As we know that, R=R∘(1+α∆T) Ω ............(1) We have R0 =18.33Ω α=0.0045∘C-1 ∆T=(16385∘C-20∘C) =16365∘C Putting these values in Equation (1), we get R=R∘(1+α∆T) ΩR=18.33*(1+0.0045∘C-1*16365∘C) ΩR=1368.33Ω Hence, Resistance of light bulb will be 1368.33Ω.

Engineering

Electrical Engineering

(a) Initially, the temperature of the filament is 20°C and there is no current flowing through it. What is the resistance of the light bulb under these conditions? (b) If a voltage is applied across the terminals of the light bulb, current begins to flow through it. The temperature T of the filament increases linearly with the current I through it, according to the equation T(1) = (2500°C A-¹)I + 20°C. What is the current through the light bulb when the voltage across its terminals is 120 V? (Hint: Use the equation given in this part to determine the resistance of the light bulb as a function of current. Substitute that result into the equation V = IR, and solve for the current I.) (c) What is the temperature of the filament when the voltage across it is 120 V? (d) What is the resistance of the light bulb when the voltage across its terminals is 120 V? Compare your result with the room-temperature, zero-current resistance you found in Part (a). .

(a) Initially, the temperature of the filament is 20°C and there is no current flowing through it. What is the resistance of the light bulb under these conditions? (b) If a voltage is applied across the terminals of the light bulb, current begins to flow through it. The temperature T of the filament increases linearly with the current I through it, according to the equation T(1) = (2500°C A-¹)I + 20°C. What is the current through the light bulb when the voltage across its terminals is 120 V? (Hint: Use the equation given in this part to determine the resistance of the light bulb as a function of current. Substitute that result into the equation V = IR, and solve for the current I.) (c) What is the temperature of the filament when the voltage across it is 120 V? (d) What is the resistance of the light bulb when the voltage across its terminals is 120 V? Compare your result with the room-temperature, zero-current resistance you found in Part (a). .

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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