Find the neutral temperature and inversion temperature of
Question: Find the neutral temperature and inversion temperature of copper-iron thermocouple if the reference junction is kept at $0^{\circ} \mathrm{C} .$ Use the data in table (33.1). Solution:...
Read More →Find the thermo-emf developed in a copper-silver thermocouple
Question: Find the thermo-emf developed in a copper-silver thermocouple when the junctions are kept at $0^{\circ} \mathrm{C}$ and $40^{\circ} \mathrm{C} .$ Use the data in table (33.1). Solution:...
Read More →The temperatures of the junctions of a bismuth-silver
Question: The temperatures of the junctions of a bismuth-silver thermocouple are maintained at $0^{\circ} \mathrm{C}$ and $0.0011^{\circ} \mathrm{C}$. Find the thermo-emf (Seebeck emf) developed. For Bismuth-silver, $a=-46 \times 10^{-6} \mathrm{~V} / \mathrm{deg}$ and $b=-0.48 \times 10^{-6} \mathrm{~V} / \mathrm{deg}^{2}$. Solution:...
Read More →The 2.0 Ω resistor shown in figure is dipped into a calorimeter containing water.
Question: The $2.0 \Omega$ resistor shown in figure is dipped into a calorimeter containing water. The heat capacity of the calorimeter together with water is $2000 \mathrm{~J} / \mathrm{K}$. (a) If the circuit is active for 15 minutes, what would be the rise in the temperature of the water? (b) Suppose the $6.0 \Omega$ resistor gets burnt. What would be the rise in the temperature of the water in the next 15 minutes? Solution:...
Read More →Using Rolle's theorem, find the point on the curve
Question: Using Rolle's theorem, find the point on the curve $y=x(x-4), x \in[0,4]$, where the tangent is parallel to the x-axis. Solution:...
Read More →The coil of an electric bulb takes 40 watts to start glowing.
Question: The coil of an electric bulb takes 40 watts to start glowing. If more than $40 \mathrm{~W}$ is supplied, $60 \%$ of the extra power is converted into light and the remaining into heat. The bulb consumes $100 \mathrm{~W}$ at $220 \mathrm{~V}$. Find the percentage drop in the light intensity at a point if the supply voltage changes from $220 \mathrm{~V}$ to $200 \mathrm{~V}$. Solution:...
Read More →Discuss the applicability for Rolle's theorem, when:
Question: Discuss the applicability for Rolle's theorem, when: $f(x)=[x]$ on $[-1,1]$, where $[x]$ denotes the greatest integer not exceeding $x$ Solution:...
Read More →An electric kettle used to prepare tea,
Question: An electric kettle used to prepare tea, takes 2 minutes to boil 4 cups of water ( 1 cup contains 200 cc of water) is the room temperature is $25^{\circ} \mathrm{C}$. (a) If the cost of power consumption is Rs $1.00$ per unit ( 1 unit=1000 watt-hour), calculate the cost of boiling 4 cups of water. (b) What will be the corresponding cost if the room temperature drops to $5^{\circ} \mathrm{C}_{\text {? }}$ ? Solution:...
Read More →Discuss the applicability for Rolle's theorem, when:
Question: Discuss the applicability for Rolle's theorem, when: $f(x)=\cos \frac{1}{x}$ on $[-1,1]$ Solution:...
Read More →An immersion heater rated 1000W,
Question: An immersion heater rated $1000 \mathrm{~W}, 220 \mathrm{~V}$ is used to heat $0.01 \mathrm{~m}^{3}$ of water. Assuming that the power is supplied at $220 \mathrm{~V}$ and $60 \%$ of the power supplied is used to heat the water, how long will it take to increase the temperature of the water from $15^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}_{?}$ Solution:...
Read More →Discuss the applicability for Rolle's theorem, when:
Question: Discuss the applicability for Rolle's theorem, when: $f(x)=2+(x-1)^{2 / 3}$ on $[0,2]$ Solution:...
Read More →An electric bulb marked 220V,
Question: An electric bulb marked $220 \mathrm{~V}, 100 \mathrm{~W}$ will get fused if it is made to consume $150 \mathrm{~W}$ or more. What voltage fluctuation will the bulb withstand? Solution:...
Read More →A servo voltage stabilizer restricts the voltage output to
Question: A servo voltage stabilizer restricts the voltage output to $220 \mathrm{~V} \pm 1 \%$. If an electric bulb rated at $220 \mathrm{~V}, 100 \mathrm{~W}$ is connected to it, what will be the minimum and maximum power consumed by it? Solution:...
Read More →Discuss the applicability for Rolle's theorem, when:
Question: Discuss the applicability for Rolle's theorem, when: $f(x)=x^{1 / 2}$ on $[-1,1]$ Solution:...
Read More →An electric bulb, when connected across a power supply of
Question: An electric bulb, when connected across a power supply of $220 \mathrm{~V}$, consumes a power of $60 \mathrm{~W}$. If the supply drops to $180 \mathrm{~V}$, what will be the power consumed? If the power supply is suddenly increased to $240 \mathrm{~V}$, what will be the power consumed? Solution:...
Read More →A bulb with rating 250V,
Question: A bulb with rating $250 \mathrm{~V}, 100 \mathrm{~W}$ is connected to a power supply of $220 \mathrm{~V}$ situated $10 \mathrm{~m}$ away using a copper wire of area pf cross-section $5 \mathrm{~mm}^{2}$. How much power will be consumed by the connecting wires? Resistivity of copper $=1.7 \times 10^{-8} \Omega-m$. Solution:...
Read More →Discuss the applicability for Rolle's theorem, when:
Question: Discuss the applicability for Rolle's theorem, when: $f(x)=(x-1)(2 x-3)$, where $1 \leq x \leq 3$ Solution:...
Read More →A heater-coil is to be constructed with a nichrome wire
Question: A heater-coil is to be constructed with a nichrome wire $\left(\rho=1.0 \times 10^{-6} \Omega-\mathrm{m}\right)$ which can operate at $500 \mathrm{~W}$ when connected to a $250 \mathrm{~V}$ supply. (a) What would be the resistance of the coil? (b) If the cross-sectional area of the wire is $0.5 \mathrm{~mm}{ }^{2}$, what length of the wire will be needed? (c) If the radius of each turn is $4.0 \mathrm{~mm}$, how many turns will be there in the coil? Solution:...
Read More →The specification on a heater coil is 250V, 500W.
Question: The specification on a heater coil is $250 \mathrm{~V}, 500 \mathrm{~W}$. Calculate the resistance of the coil. What will be the resistance of the coil of $1000 \mathrm{~W}$ to operate at the same voltage? Solution:...
Read More →Verify Rolle's theorem for each of the following functions:
Question: Verify Rolle's theorem for each of the following functions: Show that $f(\mathrm{x})=\mathrm{x}(\mathrm{x}-5)^{2}$ satisfies Rolle's theorem on $[0,5]$ and that the value of $c$ is $(5 / 3)$ Solution:...
Read More →A coil of resistance
Question: A coil of resistance $100^{\Omega}$ is connected across a battery of emf $6.0 \mathrm{~V}$. Assume that the heat developed in the coil is used to raise its temperature. If the heat capacity of the coil is $4.0 \mathrm{~J} / \mathrm{K}$, how long will it take to raise the temperature of the coil by 15 ${ }^{\circ} \mathrm{C}_{\text {? }}$ Solution:...
Read More →An electric current of 2.0A passes through a wire of
Question: An electric current of $2.0$ A passes through a wire of resistance $25^{\Omega}$. How much heat will be developed in minute? Solution:...
Read More →Verify Rolle's theorem for each of the following functions:
Question: Verify Rolle's theorem for each of the following functions: $f(x)=x(x+2) e^{x}$ in $[-2,0]$ Solution:...
Read More →Verify Rolle's theorem for each of the following functions:
Question: Verify Rolle's theorem for each of the following functions: $f(x)=\sin x-\sin 2 x$ in $[0,2 \pi]$ Solution:...
Read More →Verify Rolle's theorem for each of the following functions:
Question: Verify Rolle's theorem for each of the following functions: $f(x)=e^{-x}(\sin x-\cos x)$ in $\left[\frac{\pi}{4}, \frac{5 \pi}{4}\right]$ Solution:...
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