Question

Two conductors have the same resistance a 0°C but their temperature coefficients o resistance are α₁ and α₂. The respective temperature coefficients of their series parallel combinations are nearly

$fraction numerator straight alpha subscript 1 space plus straight alpha subscript 2 over denominator 2 end fraction comma space fraction numerator straight alpha subscript 1 space plus space straight alpha subscript 2 over denominator 2 end fraction$
$fraction numerator straight alpha subscript 1 space plus straight alpha subscript 2 over denominator 2 end fraction comma space straight alpha subscript 1 space plus straight alpha subscript 2$
$space straight alpha subscript 1 space plus straight alpha subscript 2 comma space fraction numerator straight alpha subscript 1 space plus straight alpha subscript 2 over denominator 2 end fraction$
$straight alpha subscript 1 space plus straight alpha subscript 2 space comma space fraction numerator straight alpha subscript 1 straight alpha subscript 2 over denominator straight alpha subscript 1 space plus straight alpha subscript 2 end fraction$

Solution

fraction numerator straight alpha subscript 1 space plus straight alpha subscript 2 over denominator 2 end fraction comma space fraction numerator straight alpha subscript 1 space plus space straight alpha subscript 2 over denominator 2 end fraction

R_e = R_o +R_o
2R(1 + α_sΔT)
= R( 1 +α₁ΔT) + R(1+α₂ΔT)
= α_s = α₁+α₂ / 2
R_p = R x R / R+R
$straight R over 2 left parenthesis space 1 space plus space straight alpha subscript straight p increment straight T right parenthesis space equals space fraction numerator straight R space left parenthesis 1 space plus straight alpha subscript 1 increment straight T right parenthesis space straight x space straight R left parenthesis space 1 space plus space straight alpha subscript 2 increment straight T right parenthesis over denominator straight R space left parenthesis 1 space plus straight alpha subscript 1 increment straight T right parenthesis space plus space straight R left parenthesis space 1 space plus space straight alpha subscript 2 increment straight T right parenthesis end fraction fraction numerator begin display style 1 space plus space straight alpha subscript straight p increment straight T end style over denominator 2 end fraction space equals space open parentheses 1 space plus space straight alpha subscript 1 increment straight T close parentheses left parenthesis 1 space plus space straight alpha subscript 2 increment straight T right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket space 1 space plus space left parenthesis straight alpha subscript 1 space plus space straight alpha subscript 2 right parenthesis increment straight T right square bracket to the power of negative 1 end exponent space equals space left square bracket 1 space plus space left parenthesis straight alpha subscript 1 space plus straight alpha subscript 2 right parenthesis increment straight T right square bracket space left square bracket 2 space plus space open parentheses straight alpha subscript 1 space plus space straight alpha subscript 2 right parenthesis increment straight T close parentheses to the power of negative 1 end exponent space equals space 1 half space left square bracket space 1 space plus space left parenthesis straight alpha subscript 1 space plus space straight alpha subscript 2 right parenthesis space increment straight T right square bracket space open square brackets 1 minus fraction numerator left parenthesis straight alpha subscript 1 space plus space straight alpha subscript 2 right parenthesis over denominator 2 end fraction increment straight T close square brackets fraction numerator 1 space plus space straight alpha subscript straight p increment straight T over denominator 2 end fraction space equals space open square brackets 1 plus fraction numerator begin display style left parenthesis straight alpha subscript 1 space plus space straight alpha subscript 2 right parenthesis end style over denominator begin display style 2 end style end fraction increment straight T close square brackets straight alpha subscript straight p space equals space fraction numerator straight alpha subscript 1 space plus straight alpha subscript 2 over denominator 2 end fraction$

For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

Some More Questions From Mechanical Properties of Fluids Chapter

What is an oscillatory motion?

What is time period?

Define frequency.

What is the condition for motion to be simple harmonic motion?

In the displacement equation y = r sin(ωt/ + ϕ) what does ϕ called and what information does it give?

What determines the natural frequency of an oscillator?

Is there any relation between uniform circular motion and simple harmonic motion?

What is periodic motion?

Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction