Idea of Temperature

Q. The charge flowing through a resistance $R$ varies with time $t$ as $Q=at-b{t}^2$, where $a$ and $b$ are positive constants. The total heat produced in $R$ is:

1. $\frac{a^{3}R}{6b}$
2. $\frac{a^{3}R}{3b}$
3. $\frac{a^{3}R}{2b}$
4. $\frac{a^{3}R}{b}$

Q. The balancing length for a cell is $560\text{cm}$ in a potentiometer experiment. When an external resistance of $10\Omega$ is connected in parallel to the cell, the balancing length changes by $60\text{cm}$. If the internal resistance of the cell is $\frac{N}{10}\Omega ,$ where N is an integer, then the value of N is .

Q. A platinum wire has a resistance of $10\Omega$ at $0^{\circ }C$ and $20\Omega$ at ${273}^{\circ }C$. Find the value of temperature coefficient of platinum.

1. $\frac{1^{\circ }}{273}{C}^{-1}$
2. $\frac{1^{\circ }}{273}{K}^{-1}$
3. $\frac{1^{\circ }}{546}{K}^{-1}$
4. $\frac{1^{\circ }}{546}{C}^{-1}$

Q. In the arrangement shown in the figure when the switch $S_2$ is open, the galvanometer shows no deflection for $l=\frac{L}{2}$. When the switch $S_2$ is closed, the galvanometer shows no deflection for $l=\frac{5L}{12}$. The internal resistance $\left(r\right)$ of $6\text{V}$ cell, and the emf $E$ of the other battery are respectively

1. $3\Omega$, $8\text{V}$
2. $2\Omega$, $12\text{V}$
3. $2\Omega$, $24\text{V}$
4. $3\Omega$, $12\text{V}$

Q. The amount of heat generated in a coil of resistance $R$ due to a charge $q$ passing through it if the current in the coil, decreases down to $0$ uniformly during a time internal $t_o$ is -

1. $\frac{2}{3}\frac{q^{2}R}{t_o}$
2. $\frac{4}{3}\frac{q^{2}R}{t_o}$
3. $\frac{1}{3}\frac{q^{2}R}{t_o}$
4. $\frac{4}{3}\frac{q{R}^2}{t_o}$

Q. Resistance of a resistor at temperature $t$ ${}^o\text{C}$ is $R_t=R_0(1+\alpha t+\beta t^2)$, where $R_0$ is the resistance at $0{}^o\text{C}$. The temperature coefficient of resistance at temperature $t{}^o\text{C}$ is

1. $\frac{(1+\alpha t+\beta t^2)}{\alpha +2\beta t}$
2. $(\alpha +2\beta t)$
3. $\frac{\alpha +2\beta t}{(1+\alpha t+\beta t^2)}$
4. $\frac{\alpha +2\beta t}{2(1+\alpha t+\beta t^2)}$

Q. A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to this current, the temperature of the wire is raised by $\Delta T$ in a time $t$. A number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of wire is raised by same amount $\Delta T$ in the same time $t$. Find the value of $N$.

1. $4$
2. $6$
3. $8$
4. $2$

Q. A wire $X$ of half the diameter and half the length as of a wire $Y$ of similar material. The ratio of resistances of $X$ to that of $Y$ is -

1. $8:1$
2. $4:1$
3. $2:1$
4. $1:1$

Q. The same mass of copper is drawn into two wires $A$ and $B$ of radii $r$ and $3r$ respectively. They are connected in series, and electric current is passed. The ratio of the heat proiduced in $A$ and $B$ is :

1. $1:9$
2. $1:81$
3. $81:1$
4. $9:1$

Q. A $5.0\mu \text{F}$ capacitor having a charge of $20\mu \text{C}$ is discharged through a wire of resistance of $5.0\Omega$. Find the heat dissipated in the wire between $25\mu \text{s}$ to $50\mu \text{s}$ after the connections are made. (Take, $1/e^2=0.135)$

1. $4.7\mu \text{J}$
2. $3.7\mu \text{J}$
3. $5.7\mu \text{J}$
4. $2.7\mu \text{J}$

Q. Two resistors with temperature coefficient of resistance ${\alpha }_1$ and ${\alpha }_2$ have resistance $R_1$ and $R_2$ at $0^{\circ }C$. The temperature coefficient of the compound resistor consisting of the two resistors connected in parallel

1. $\frac{{\alpha }_1+{\alpha }_2}{2}$
2. $\frac{2{\alpha }_1{\alpha }_2}{{\alpha }_1+{\alpha }_2}$
3. $\frac{R_1{\alpha }_1+R_2{\alpha }_2}{R_1+R_2}$
4. $\frac{R_1{\alpha }_2+R_2{\alpha }_1}{R_1+R_2}$

Q. The temperature coefficient of resistance of a conductor varies as $\alpha \left(T\right)=3T^2+2T$. If $R_0$ is resistance at $T=0$ and $R$ is resistance at $T$, then

1. $R=R_0(6T+2)$
2. $R=2R_0(3+2T)$
3. $R=R_0(1+T^2+T^3)$
4. $R=R_0(1-T+T^2+T^3)$

Q. The charge flowing through a resistance $R$ varies with time as $Q=at-b{t}^2$, where $a$ and $b$ are positive constants. The total heat produced in $R$ for the time interval $t=0$ to time when current is zero for the first time is -

1. $\frac{a^{3}R}{6b}$
2. $\frac{a^{3}R}{3b}$
3. $\frac{a^{3}R}{2b}$
4. $\frac{a^{3}R}{b}$

Q. The initial connection of the two capacitors are shown below. The heat energy dissipated until the system achieves its steady state is

1. $\frac{C{V}^2}{7}$
2. $\frac{3C{V}^2}{5}$
3. $\frac{5C{V}^2}{11}$
4. $\frac{9C{V}^2}{22}$

Q. Resistance of a resistor at temperature $t^{\circ }C$ is $R_t=R_0(1+at+b{t}^2)$; where $R_0$ is the resistance at $0^{\circ }C.$ The temperature coefficient of resistance at temperature $t^{\circ }C$ is

1. $(a+2bt)$
2. $\frac{(1+at+b{t}^2)}{a+2bt}$
3. $\frac{a+2bt}{(1+at+b{t}^2)}$
4. $\frac{a+2bt}{2(1+at+b{t}^2)}$

Q. One of the circuits for the measurement of resistance using potentiometer is as shown. The galvanometer is connected at point $A$ and zero deflection is observed at length $PJ=30\text{cm}.$ In second case the secondary cell is changed and the zero deflection is observed at length $PJ=10\text{cm}.$The resistance $R$ (in ohm) is?
For $1^{st}\text{case},$ take ${ϵ}_s=10\text{V}$ and $r=1\Omega$ and for $2^{nd}\text{case},$ take ${ϵ}_s=5\text{V}$ and $r=2\Omega$

Q. A wire breaks when subjected to a stress $S$. If $\rho$ is the density of the material of the wire and $g$, the acceleration due to gravity, then the length of the wire so that it breaks by its own weight is :

1. $\rho /gs$
2. $gs/\rho$
3. $s/\rho g$
4. $\rho gs$

Q. Compute the greatest length of steel wire that can hang vertically without breaking under its own weight. (Breaking stress of steel wire $7.2\times {10}^{8}N/m^2$, density of steel $=7800kg/m^3$)

Q. An elevator cable is to have a maximum stress of $7\times {10}^{7}n/m^2$ to allow for appropriate safety factors. Its maximum upward acceleration is $1.5m/s^2$. If the cable has to support the total weight of $2000kg$ of a loaded elevator, the area of cross-section of the cable should be

1. $3.22c{m}^2$
2. $2.38c{m}^2$
3. $8.23c{m}^2$
4. $0.32c{m}^2$

Q. The separation between the plates of a charged parallel-plate capacitor is increased. Which of the following quantities will change?

1. Charge on the capacitor
2. Potential difference across the capacitor
3. Energy density between the plates
4. None of these

Q. What would be the greatest length of a steel wire, which when fixed at one end can hang freely without breaking (Density of steel = $7800kg/m^3$ and Breaking stress = $7.8 \times 10^8 N/m^2)

1. 1000 m
2. 10, 000 m
3. 7, 000 m
4. 700 m

Q. A copper and a steel wire of the same diameter are connected end to end. A deforming force $F$ is applied to this composite wire which causes a total elongation of $1cm$. The two wires will have then

1. the same stress but different strain
2. the same strain but different stress
3. the same stress and strain
4. different strains and stress

Q. A steel wire AB of length 100 cm is fixed rigidly at points A and B in an aluminium frame as shown in the figure If the temperature of the system increases through 100C, then the excess stress produced in the steel wire relative to the aluminium? ${\alpha }_{\mu }=22\times {10}^{-6}{/}^{0}Cand{\alpha }_{stret}=11\times {10}^{-6}{/}^{0}C$ young 's modulus of steel is $2\times {10}^{31}{Nm}^{-2}$

1. $2.2\times {10}^5$Pa
2. $22\times {10}^{27}$Pa
3. $2.2\times {10}^2$Pa
4. $220\times {10}^2$Pa

Q. In a mechanical refrigerator, the temperature coils are at a temperature $-{23}^{0}C$ and the compressed gas in condenser has a temperature of ${27}^{0}C$. Theoretical coefficient of performance is:

1. $10$
2. $8$
3. $5$
4. $6.5$

Q. The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than $1240nm$, is incident on it. The band gap for the semiconductor is:

1. $2.1eV$
2. $2.5eV$
3. $1eV$
4. $0.7eV$

Q. For steel, the breaking stress is $6\times {10}^{6}N/m^2$ and the density is $8\times {10}^{3}kg/m^3$. The maximum length of steel wire, which can be suspended without breaking under its own weight is ($g=10m/s^2$)

1. $140m$
2. $120m$
3. $75m$
4. $200m$

Q. In the arrangement shown in figure, when switch $S$ is closed, find the final charge on the $6\mu F$ capacitor :

1. $12\mu C$
2. $24\mu C$
3. $32\mu C$
4. $48\mu C$

Q. A bar weighing 100 N hinged at one end and the end is tied to a vertical string which keeps the bar horizontal. The tension in the string in nearer to

1. $500N$
2. $100N$
3. $50N$
4. $10N$

Q. A platinum wire has a resistance of $10\Omega$ at $0^{\circ }C$ and $20\Omega$ at ${273}^{\circ }C$. Find the value of temperature coefficient of platinum.

1. $\frac{1^{\circ }}{273}{C}^{-1}$
2. $\frac{1^{\circ }}{273}{K}^{-1}$
3. $\frac{1^{\circ }}{546}{C}^{-1}$
4. $\frac{1^{\circ }}{546}{K}^{-1}$

Q. In an experiment to measure the internal resistance of a cell by a potentiometer, it is found that the balance point is at a length of $2\text{m}$ when the cell is shunted by a $5\Omega$ resistance and is at a length of $3\text{m}$ when the cell is shunted by a $10\Omega$ resistance, then the internal resistance of the cell is

1. $1.5\Omega$
2. $10\Omega$
3. $15\Omega$
4. $1\Omega$