Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Electric Current in Conductors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Current in Conductors

At 20^ ^ ^ C , an iron wire and a copper wire have resistances of...

At 20^{}^{{}^{\circ}} \text{C}, an iron wire and a copper wire have resistances of 3.9Ω3.9 \Omega and 4.1Ω4.1 \Omega, respectively. Determine the temperature at which their resistances become equal. The temperature coefficient of resistivity is 5.0×10−3 K−15.0 \times 10^{-3} \text{ K}^{-1} for iron and 4.0×10−3 K−14.0 \times 10^{-3} \text{ K}^{-1} for copper. Ignore any effects of thermal expansion.

Options

  1. A74.5^{}^{{}^{\circ}} \text{C}
  2. B64.5^{}^{{}^{\circ}} \text{C}
  3. C84.5^{}^{{}^{\circ}} \text{C}
  4. D94.5^{}^{{}^{\circ}} \text{C}

Correct answer

C. 84.5^{}^{{}^{\circ}} \text{C}

Step-by-step solution

Let the initial temperature be T_0 = 20^{}^{{}^{\circ}} \text{C} and the final temperature be TT.

The resistance of a wire at temperature TT is given by R=R0[1+α(T−T0)]R = R_0[1 + \alpha(T - T_0)].

For the iron wire:
RFe=3.9[1+5.0×10−3(T−20)]R_{Fe} = 3.9 [1 + 5.0 \times 10^{-3} (T - 20)]

For the copper wire:
RCu=4.1[1+4.0×10−3(T−20)]R_{Cu} = 4.1 [1 + 4.0 \times 10^{-3} (T - 20)]

Equating the two resistances:
3.9[1+5.0×10−3(T−20)]=4.1[1+4.0×10−3(T−20)]3.9 [1 + 5.0 \times 10^{-3} (T - 20)] = 4.1 [1 + 4.0 \times 10^{-3} (T - 20)]

3.9+19.5×10−3(T−20)=4.1+16.4×10−3(T−20)3.9 + 19.5 \times 10^{-3} (T - 20) = 4.1 + 16.4 \times 10^{-3} (T - 20)

(19.5−16.4)×10−3(T−20)=4.1−3.9(19.5 - 16.4) \times 10^{-3} (T - 20) = 4.1 - 3.9

3.1×10−3(T−20)=0.23.1 \times 10^{-3} (T - 20) = 0.2

T - 20 = \dfrac{0.2}{3.1 \times 10^{-3}} = \dfrac{200}{3.1} \approx 64.5^{}^{{}^{\circ}} \text{C}

T = 20 + 64.5 = 84.5^{}^{{}^{\circ}} \text{C}
Practice Electric Current in Conductors on Quantrex Academy →

More from Electric Current in Conductors

The amount of charge passing through a cross-section of a wire in time t is given by Q(t)… Concepts Of Physics MCQ Edition [Volume 2]A discharge tube carries an electric current of 2.0 . Determine the amount of charge that… Concepts Of Physics MCQ Edition [Volume 2]The current flowing through a wire varies with time according to i = i_0 + α t , where… Concepts Of Physics MCQ Edition [Volume 2]A copper wire with a cross-section of 1.0 mm^2 carries a current of 1.0 A . Determine the… Concepts Of Physics MCQ Edition [Volume 2]An electron gun releases 2.0 × 10^ 16 electrons per second. Determine the electric… Concepts Of Physics MCQ Edition [Volume 2]The amount of charge passing through a cross-section of a wire in time t is Q(t) = At^2 +… Concepts Of Physics MCQ Edition [Volume 2]A uniform wire having a resistance of 100 Ω is melted and recast into a new wire whose… Concepts Of Physics MCQ Edition [Volume 2]Determine the required length of a copper wire having a cross-sectional area of 0.01 mm^2… Concepts Of Physics MCQ Edition [Volume 2] Full Electric Current in Conductors list All Concepts Of Physics MCQ Edition [Volume 2] PYQs