Answer
397.2k+ views
Hint:Use the formula for power in terms of the current and resistance. Also use the formula for power in terms of the change in heat and time interval. Use the formula for the heat exchanged for a substance. This formula gives the relation between mass of the substance, specific heat of the substance and change in temperature of the substance.
Formulae used:
The power \[P\] is given by
\[P = {I^2}R\] …… (1)
Here, \[I\] is the current and \[R\] is the resistance.
The power \[P\] is given by
\[P = \dfrac{{\Delta Q}}{{\Delta t}}\] …… (2)
Here, \[\Delta Q\] is the change in the heat in the time interval \[\Delta t\].
The heat exchanged \[\Delta Q\] is given by
\[\Delta Q = mc\Delta T\] …… (3)
Here, \[m\] is the mass of the substance, \[c\] is specific heat of the substance and \[\Delta T\] is a change in temperature of the substance.
Complete step by step answer:
We have given that the heat capacity of the calorimeter is \[50\,{\text{J}} \cdot ^\circ {{\text{C}}^{ - 1}}\] and the specific heat capacity of the liquid is \[450\,{\text{J}} \cdot {\text{k}}{{\text{g}}^{{\text{ - 1}}}} \cdot ^\circ {{\text{C}}^{ - 1}}\].
\[c = 50\,{\text{J}} \cdot ^\circ {{\text{C}}^{ - 1}}\]
\[\Rightarrow{c_L} = 450\,{\text{J}} \cdot {\text{k}}{{\text{g}}^{{\text{ - 1}}}} \cdot ^\circ {{\text{C}}^{ - 1}}\]
The mass of the liquid in the calorimeter is \[1\,{\text{kg}}\].
\[m = 1\,{\text{kg}}\]
The change in the temperature of the liquid is \[10^\circ {\text{C}}\] and the current passed through the calorimeter is \[2.0\,{\text{A}}\] for 10 minutes.
\[\Delta T = 10^\circ {\text{C}}\]
\[\Rightarrow I = 2.0\,{\text{A}}\]
\[\Rightarrow \Delta t = 10\,{\text{min}}\]
Convert the unit of the time to the SI system of units.
\[\Delta t = \left( {10\,{\text{min}}} \right)\left( {\dfrac{{60\,{\text{s}}}}{{1\,{\text{min}}}}} \right)\]
\[ \Rightarrow \Delta t = 600\,{\text{s}}\]
We have asked to calculate the resistance of the coil.
Substitute \[{I^2}R\] for \[P\] in equation (2).
\[{I^2}R = \dfrac{{\Delta Q}}{{\Delta t}}\]
Rearrange the above equation for \[R\].
\[R = \dfrac{{\Delta Q}}{{{I^2}\Delta t}}\]
Substitute \[m{c_{net}}\Delta T\] for \[\Delta Q\] in the above equation.
\[R = \dfrac{{m{c_{net}}\Delta T}}{{{I^2}\Delta t}}\]
The net specific heat capacity of the system is the sum of the specific heat capacity of the calorimeter and the liquid in the calorimeter.
\[{c_{net}} = c + {c_L}\]
Substitute \[c + {c_L}\] for \[{c_{net}}\] in the above equation.
\[R = \dfrac{{m\left( {c + {c_L}} \right)\Delta T}}{{{I^2}\Delta t}}\]
Substitute \[1\,{\text{kg}}\] for \[m\], \[50\,{\text{J}} \cdot ^\circ {{\text{C}}^{ - 1}}\] for \[c\], \[450\,{\text{J}} \cdot {\text{k}}{{\text{g}}^{{\text{ - 1}}}} \cdot ^\circ {{\text{C}}^{ - 1}}\] for \[{c_L}\], \[10^\circ {\text{C}}\] for \[\Delta T\], \[2.0\,{\text{A}}\] for \[I\] and \[600\,{\text{A}}\] for \[\Delta t\] in the above equation.
\[R = \dfrac{{\left( {1\,{\text{kg}}} \right)\left[ {\left( {50\,{\text{J}} \cdot ^\circ {{\text{C}}^{ - 1}}} \right) + \left( {450\,{\text{J}} \cdot {\text{k}}{{\text{g}}^{{\text{ - 1}}}} \cdot ^\circ {{\text{C}}^{ - 1}}} \right)} \right]\left( {10^\circ {\text{C}}} \right)}}{{{{\left( {2.0\,{\text{A}}} \right)}^2}\left( {600\,{\text{A}}} \right)}}\]
\[ \Rightarrow R = 2.08\,\Omega \]
\[ \therefore R \approx 2.1\,\Omega \]
Hence, the resistance of the coil is \[2.1\,\Omega \].
Note: The students should not forget to convert the unit of the time for which the current is passed through the calorimeter in the SI system of units. The students should also not forget to take the sum of the specific heats of the calorimeter and the liquid in the calorimeter. If this net specific heat of the system is not taken then the final answer will be incorrect.
Formulae used:
The power \[P\] is given by
\[P = {I^2}R\] …… (1)
Here, \[I\] is the current and \[R\] is the resistance.
The power \[P\] is given by
\[P = \dfrac{{\Delta Q}}{{\Delta t}}\] …… (2)
Here, \[\Delta Q\] is the change in the heat in the time interval \[\Delta t\].
The heat exchanged \[\Delta Q\] is given by
\[\Delta Q = mc\Delta T\] …… (3)
Here, \[m\] is the mass of the substance, \[c\] is specific heat of the substance and \[\Delta T\] is a change in temperature of the substance.
Complete step by step answer:
We have given that the heat capacity of the calorimeter is \[50\,{\text{J}} \cdot ^\circ {{\text{C}}^{ - 1}}\] and the specific heat capacity of the liquid is \[450\,{\text{J}} \cdot {\text{k}}{{\text{g}}^{{\text{ - 1}}}} \cdot ^\circ {{\text{C}}^{ - 1}}\].
\[c = 50\,{\text{J}} \cdot ^\circ {{\text{C}}^{ - 1}}\]
\[\Rightarrow{c_L} = 450\,{\text{J}} \cdot {\text{k}}{{\text{g}}^{{\text{ - 1}}}} \cdot ^\circ {{\text{C}}^{ - 1}}\]
The mass of the liquid in the calorimeter is \[1\,{\text{kg}}\].
\[m = 1\,{\text{kg}}\]
The change in the temperature of the liquid is \[10^\circ {\text{C}}\] and the current passed through the calorimeter is \[2.0\,{\text{A}}\] for 10 minutes.
\[\Delta T = 10^\circ {\text{C}}\]
\[\Rightarrow I = 2.0\,{\text{A}}\]
\[\Rightarrow \Delta t = 10\,{\text{min}}\]
Convert the unit of the time to the SI system of units.
\[\Delta t = \left( {10\,{\text{min}}} \right)\left( {\dfrac{{60\,{\text{s}}}}{{1\,{\text{min}}}}} \right)\]
\[ \Rightarrow \Delta t = 600\,{\text{s}}\]
We have asked to calculate the resistance of the coil.
Substitute \[{I^2}R\] for \[P\] in equation (2).
\[{I^2}R = \dfrac{{\Delta Q}}{{\Delta t}}\]
Rearrange the above equation for \[R\].
\[R = \dfrac{{\Delta Q}}{{{I^2}\Delta t}}\]
Substitute \[m{c_{net}}\Delta T\] for \[\Delta Q\] in the above equation.
\[R = \dfrac{{m{c_{net}}\Delta T}}{{{I^2}\Delta t}}\]
The net specific heat capacity of the system is the sum of the specific heat capacity of the calorimeter and the liquid in the calorimeter.
\[{c_{net}} = c + {c_L}\]
Substitute \[c + {c_L}\] for \[{c_{net}}\] in the above equation.
\[R = \dfrac{{m\left( {c + {c_L}} \right)\Delta T}}{{{I^2}\Delta t}}\]
Substitute \[1\,{\text{kg}}\] for \[m\], \[50\,{\text{J}} \cdot ^\circ {{\text{C}}^{ - 1}}\] for \[c\], \[450\,{\text{J}} \cdot {\text{k}}{{\text{g}}^{{\text{ - 1}}}} \cdot ^\circ {{\text{C}}^{ - 1}}\] for \[{c_L}\], \[10^\circ {\text{C}}\] for \[\Delta T\], \[2.0\,{\text{A}}\] for \[I\] and \[600\,{\text{A}}\] for \[\Delta t\] in the above equation.
\[R = \dfrac{{\left( {1\,{\text{kg}}} \right)\left[ {\left( {50\,{\text{J}} \cdot ^\circ {{\text{C}}^{ - 1}}} \right) + \left( {450\,{\text{J}} \cdot {\text{k}}{{\text{g}}^{{\text{ - 1}}}} \cdot ^\circ {{\text{C}}^{ - 1}}} \right)} \right]\left( {10^\circ {\text{C}}} \right)}}{{{{\left( {2.0\,{\text{A}}} \right)}^2}\left( {600\,{\text{A}}} \right)}}\]
\[ \Rightarrow R = 2.08\,\Omega \]
\[ \therefore R \approx 2.1\,\Omega \]
Hence, the resistance of the coil is \[2.1\,\Omega \].
Note: The students should not forget to convert the unit of the time for which the current is passed through the calorimeter in the SI system of units. The students should also not forget to take the sum of the specific heats of the calorimeter and the liquid in the calorimeter. If this net specific heat of the system is not taken then the final answer will be incorrect.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)