Resistance of a resistor at temperature t° C is Rt=R0(1+α t+β t2) Here R0 is the resistance at 0 ° C. The temperature coefficient of resistance at temperature t° C is

Question

Resistance of a resistor at temperature t° C is Rt=R0(1+α t+β t2) Here R0 is the resistance at 0 ° C. The temperature coefficient of resistance at temperature t° C is (A) ((1+α t+β t2)/α+2 β t) (B) (α+2 β t) (C) (α+2 β t/(1+α t+β t2)) (D) ((α+2 β t)/2(1+α t+β t))

Tardigrade Admin · Accepted Answer

Temperature coefficient of resistance =(1/Rt) (dR/d t) =(1/R0(1+α t+β t2) d t) R0(1+α t+β t2) =(α+2 β t/1+α t+β t2)

Q. Resistance of a resistor at temperature $t^{\circ} C$ is $R_{t} = R_{0} (1 + α t + β t^{2})$ Here $R_{0}$ is the resistance at $0^{\circ} C$ . The temperature coefficient of resistance at temperature $t^{\circ} C$ is

$\frac{( 1 + α t + β t ^{2} )}{α + 2 βt}$

$(α + 2 βt)$

$\frac{α + 2 βt}{( 1 + α t + β t ^{2} )}$

$\frac{( α + 2 βt )}{2 ( 1 + α t + βt )}$

Temperature coefficient of resistance $= \frac{1}{R _{t}} \frac{d R}{d t}$
$= \frac{1}{R _{0} ( 1 + α t + β t ^{2} ) d t} R_{0} (1 + α t + β t^{2})$
$= \frac{α + 2 βt}{1 + α t + β t ^{2}}$

Q. Resistance of a resistor at temperature t∘C is Rt​=R0​(1+αt+βt2) Here R0​ is the resistance at 0∘C. The temperature coefficient of resistance at temperature t∘C is

α+2βt(1+αt+βt2)​

(α+2βt)

(1+αt+βt2)α+2βt​

2(1+αt+βt)(α+2βt)​