An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its resistance at room temperature $\left(27.0^{\circ} C \right)$ is found to be $75.3 \Omega$. When the toaster is connected to a $230 V$ supply, the current settles, after a few seconds, to a steady value of $2.68 A$. What is the steady temperature of the nichrome element? The temperature coefficient of resistance of nichrome averaged over the temperature range involved, is $1.70 \times 10^{-4}{ }^{\circ} C ^{-1}$.
Example-(3.3)
Download our app for free and get started
When the current through the element is very small, heating effects can be ignored and the temperature $T_1$ of the element is the same as room temperature. When the toaster is connected to the supply, its initial current will be slightly higher than its steady value of $2.68 A$. But due to heating effect of the current, the temperature will rise. This will cause an increase in resistance and a slight decrease in current. In a few seconds, a steady state will be reached when temperature will rise no further, and both the resistance of the element and the current drawn will achieve steady values. The resistance $R_2$ at the steady temperature $T_2$ is
$
R_2=\frac{230 V }{2.68 A }=85.8 \Omega
$
Using the relation
$
R_2=R_1\left[1+\alpha\left(T_2-T_1\right)\right]
$
with $\alpha=1.70 \times 10^{-4}{ }^{\circ} C ^{-1}$, we get
$
T_2-T_1=\frac{(85.8-75.3)}{(75.3) \times 1.70 \times 10^{-4}}=820^{\circ} C
$
that is, $T_2=(820+27.0){ }^{\circ} C =847{ }^{\circ} C$
Thus, the steady temperature of the heating element (when heating effect due to the current equals heat loss to the surroundings) is $847^{\circ} C$.
$
R_2=\frac{230 V }{2.68 A }=85.8 \Omega
$
Using the relation
$
R_2=R_1\left[1+\alpha\left(T_2-T_1\right)\right]
$
with $\alpha=1.70 \times 10^{-4}{ }^{\circ} C ^{-1}$, we get
$
T_2-T_1=\frac{(85.8-75.3)}{(75.3) \times 1.70 \times 10^{-4}}=820^{\circ} C
$
that is, $T_2=(820+27.0){ }^{\circ} C =847{ }^{\circ} C$
Thus, the steady temperature of the heating element (when heating effect due to the current equals heat loss to the surroundings) is $847^{\circ} C$.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionIn a meter bridge, the null point is found at a distance of 40 cm from A. If a resistance of 12 Ω is connected in parallel with S, the null point occurs at 50.0 cm from. Determine the values of R and S.
- 2View SolutionDefine relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons? Use this relation to deduce the expression for the electrical resistivity of the material.
- 3A resistance of $R \Omega$ draws current from a potentiometer as shown in the figure. The potentiometer has a total resistance $R_o\Omega$ . A voltage $V$ is supplied to the potentiometer. Derive an expression for the voltage across $R$ when the sliding contact is in the middle of the potentiometer.View Solution
- 4A storage battery of emf $8.0 V$ and internal resistance $0.5\ \Omega$ is being charged by a $120 V\ dc$ supply using a series resistor of $15.5\ \Omega.$ What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?View Solution
- 5View Solution
- Write the principle of working of a metre bridge.
- In a metre bridge, the balance point is found at a distance $l_1$ with resistances R and S as shown in the figure.
An unknown resistance X is now connected in parallel to the resistance S and the balance point is found at a distance $l_2$. Obtain a formula for X in terms of $l_1$, $l_2$ and S. - 6A capacitor of capacitance $10\mu\text{F}$ is connected across a battery of emf 6.0V through a resistance of $20\text{k}\Omega$ for 4.0s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4.0s after the battery is disconnected?View Solution
- 7View SolutionTwo heated wires of the same dimensions are first connected in series and then in parallel to a source of supply. What will be the ratio of heat produced in the two cases?
- 8View Solution
- Derive an expression for drift velocity of free electrons.
- How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.
- 9View SolutionName the charge carriers of electric current in:
- Silver foil.
- Hydrogen discharge tube.
- Germanium semiconductor.
- Wire made of alloy nichrome.
- Superconductor.
- 10View Solution
- In a metre bridge [Fig. 3.27], the balance point is found to be at 39.5 cm from the end A, when the resistor Y is of $12.5\ \Omega.$ Determine the resistance of X. Why are the connections between resistors in a Wheatstone or meter bridge made of thick copper strips?
- Determine the balance point of the bridge above if X and Y are interchanged.
- What happens if the galvanometer and cell are interchanged at the balance point of the bridge? Would the galvanometer show any current?