(B) The thermoelectric $EMF$ is given by $e = \alpha t - \frac{1}{2}\beta t^2$.For the neutral temperature $t_n$,the $EMF$ is maximum,so $\frac{de}{dt

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(B) The thermoelectric $EMF$ is given by $e = \alpha t - \frac{1}{2}\beta t^2$.For the neutral temperature $t_n$,the $EMF$ is maximum,so $\frac{de}{dt} = 0$.$\frac{de}{dt} = \alpha - \beta t = 0 \Rightarrow t_n = \frac{\alpha}{\beta}$.Substituting the given values: $t_n = \frac{500}{5} = 100 \, ^\circ C$.The relationship between neutral temperature $t_n$,inversion temperature $t_i$,and cold junction temperature $t_c$ is $t_n = \frac{t_i + t_c}{2}$.Given $t_c = 0 \, ^\circ C$,we have $100 = \frac{t_i + 0}{2}$.Therefore,$t_i = 200 \, ^\circ C$.

Class 12 Physics Current Electricity Mix Examples-Current Electricity

Difficult

The thermoelectric electromotive force $e$ is given by $e = \alpha t - \frac{1}{2}\beta t^2$. If the temperature of the cold junction is $0 \, ^\circ C$,find the temperature of inversion $t_i$. (Given: $\alpha = 500.0 \, \mu V/^\circ C$,$\beta = 5.0 \, \mu V/^\circ C^2$)

A
$100 \, ^\circ C$
B
$200 \, ^\circ C$
C
$300 \, ^\circ C$
D
$400 \, ^\circ C$

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Current Electricity

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Mix Examples-Current Electricity

In the figure shown below,a resistance of $150.4\ \Omega$ is connected in series to an ammeter $A$ of resistance $240\ \Omega$. $A$ shunt resistance of $10\ \Omega$ is connected in parallel with the ammeter. The reading of the ammeter is $...\ mA$.

MediumJEE MAIN 2025

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Two bulbs of $500\, W$ and $200\, W$ are manufactured to operate on a $220\, V$ line. What is the ratio of heat produced in the $500\, W$ bulb to the $200\, W$ bulb when they are connected in parallel,and when they are connected in series?

Difficult

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Match the List-$I$ with the List-$II$ from the combination shown. In the left side (List-$I$) there are four different conditions and in the right side (List-$II$), there are ratios of heat produced in each resistance for each condition:
List-$I$ List-$II$
$(I)$ Two wires of same resistance are connected in series and same current is passed through them $(A)$ $1:2$
$(II)$ Two wires of resistance $R$ and $2R$ $\Omega$ are connected in series and same $P.D.$ is applied across them $(B)$ $4:1$
$(III)$ Two wires of same resistance are connected in parallel and same current is flowing through them $(C)$ $1:1$
$(IV)$ Two wires of resistances in the ratio $1:2$ are connected in parallel and same $P.D.$ is applied across them $(D)$ $2:1$

Difficult

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The thermo-emf of a hypothetical thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700^{\circ}C$. If the cold junction is kept at $0^{\circ}C$,then the neutral temperature is:

DifficultAP EAMCET 2011

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If the resistance of a heating coil is $484\, \Omega$ and the supply voltage is $220\, V\ AC$,how much time in $sec$ will the heater take to raise the temperature of $100\, g$ of water by $50^\circ C$?

Medium

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List-$I$	List-$II$
$(I)$ Two wires of same resistance are connected in series and same current is passed through them	$(A)$ $1:2$
$(II)$ Two wires of resistance $R$ and $2R$ $\Omega$ are connected in series and same $P.D.$ is applied across them	$(B)$ $4:1$
$(III)$ Two wires of same resistance are connected in parallel and same current is flowing through them	$(C)$ $1:1$
$(IV)$ Two wires of resistances in the ratio $1:2$ are connected in parallel and same $P.D.$ is applied across them	$(D)$ $2:1$

The thermoelectric electromotive force $e$ is given by $e = \alpha t - \frac{1}{2}\beta t^2$. If the temperature of the cold junction is $0 \, ^\circ C$,find the temperature of inversion $t_i$. (Given: $\alpha = 500.0 \, \mu V/^\circ C$,$\beta = 5.0 \, \mu V/^\circ C^2$)

Similar Questions

In the figure shown below,a resistance of $150.4\ \Omega$ is connected in series to an ammeter $A$ of resistance $240\ \Omega$. $A$ shunt resistance of $10\ \Omega$ is connected in parallel with the ammeter. The reading of the ammeter is $...\ mA$.

Two bulbs of $500\, W$ and $200\, W$ are manufactured to operate on a $220\, V$ line. What is the ratio of heat produced in the $500\, W$ bulb to the $200\, W$ bulb when they are connected in parallel,and when they are connected in series?

The thermo-emf of a hypothetical thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700^{\circ}C$. If the cold junction is kept at $0^{\circ}C$,then the neutral temperature is:

If the resistance of a heating coil is $484\, \Omega$ and the supply voltage is $220\, V\ AC$,how much time in $sec$ will the heater take to raise the temperature of $100\, g$ of water by $50^\circ C$?

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