Question

The e.m.f. in a thermoelectric circuit with one junction at $0{^\circ}C$ and the other at $t{^\circ}C$ is given by $E = At - Bt^{2}$. The neutral temperature is then

• A. $\frac{A}{B}$
• B. $- \frac{A}{2B}$
• C. $- \frac{B}{2A}$
• D. $\frac{A}{2B}$

Answer 1

Answer: (D)

$\frac{A}{2B}$

Answer 2

At neutral temperature E is maximum so

$\frac{dE}{dt} = 0$⇒ $\frac{d}{dt}(At - Bt^{2}) = 0$⇒ $A - 2Bt = 0$⇒ $t = \frac{A}{2B}$