The resistance {R_t} of a conductor varies wi | vedclass

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(B) The given equation is ${R_t} = {R_0} + {R_0}\alpha t + {R_0}\beta {t^2}$.This is a quadratic equation of the form $y = ax^2 + bx + c$,which repres

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$\alpha$ and $\beta$ are both positive

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(B) The given equation is ${R_t} = {R_0} + {R_0}\alpha t + {R_0}\beta {t^2}$.This is a quadratic equation of the form $y = ax^2 + bx + c$,which represents a parabola.From the graph,we observe that the resistance ${R_t}$ increases with temperature $t$,and the slope of the curve $\frac{dR_t}{dt} = {R_0}\alpha + 2{R_0}\beta t$ is positive and increasing.Since the curve is concave upwards,the second derivative $\frac{d^2R_t}{dt^2} = 2{R_0}\beta$ must be positive,which implies $\beta > 0$.Also,at $t = 0$,the slope is ${R_0}\alpha$. Since the curve starts with a positive slope,$\alpha$ must be positive.Therefore,both $\alpha$ and $\beta$ are positive. The correct option is $(b)$.

The resistance ${R_t}$ of a conductor varies with temperature $t$ as shown in the figure. If the variation is represented by ${R_t} = {R_0}[1 + \alpha t + \beta {t^2}]$,then

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