Answer
64.8k+ views
Hint: We will use Kirchhoff's rule to find a relation of the resistances and the $emf$ of the two batteries. Then, we will equate them with each other.
Step By Step Solution
![](https://www.vedantu.com/question-sets/807425ac-13e5-4334-92f9-6d2d11f21fdf6390817297799782169.png)
Here,
\[{V_1}\] is the $emf$ of the first battery and \[{V_2}\] is that of the second one. \[{r_1}\] is the internal resistance of the first battery and \[{r_2}\] is that of the second. \[R\] in the load resistance.
Now,
For the first situation when current is $3A$ .
By Kirchhoff’s Law,
\[\frac{{\mathop V\nolimits_1 \mathop { + V}\nolimits_2 }}{{\mathop {R + r}\nolimits_1 \mathop { + r}\nolimits_2 }} = \mathop 3\nolimits_{} \]
Thus, we can say
$\mathop {(R + r}\nolimits_1 \mathop { + r}\nolimits_2 ) = \frac{{\mathop V\nolimits_1 \mathop { + V}\nolimits_2 }}{3} \cdot \cdot \cdot \cdot (1)$
Similarly for the second case when current is $1A$ ,
$\mathop V\nolimits_1 \mathop { - V}\nolimits_2 = \mathop {R + r}\nolimits_1 \mathop { + r}\nolimits_2 $
Now,
Putting in equation $(1)$, we get
$\mathop {3V}\nolimits_1 \mathop { - 3V}\nolimits_2 = \mathop V\nolimits_1 \mathop { + V}\nolimits_2 $
After further evaluation, we get
$\mathop {2V}\nolimits_1 = \mathop {4V}\nolimits_2 $
In the question, it is asked for $\frac{{\mathop V\nolimits_1 }}{{\mathop V\nolimits_2 }}$
Thus, we get
\[\frac{{\mathop V\nolimits_1 }}{{\mathop V\nolimits_2 }} = \frac{2}{1}\]
Hence, the answer is (B).
Additional Information: The Kirchhoff’s rules are handy to use in the cases for internal resistance, multiple $emf$ and in the cases indulging potentiometer. These rules are simple and very intuitive. Just that they were placed in a standardized manner by Kirchhoff.
The internal resistance we are talking about is referring to the resistance offered by the battery itself at initiation. This internal resistance value decides about the behavior of the circuit. Though minimal, but still of concern.
Note: We directly evaluated the result due to the application of the Kirchhoff’s law. One should not be confused about the direct relation. It is trivially coming from Kirchhoff's law.
Step By Step Solution
![](https://www.vedantu.com/question-sets/807425ac-13e5-4334-92f9-6d2d11f21fdf6390817297799782169.png)
Here,
\[{V_1}\] is the $emf$ of the first battery and \[{V_2}\] is that of the second one. \[{r_1}\] is the internal resistance of the first battery and \[{r_2}\] is that of the second. \[R\] in the load resistance.
Now,
For the first situation when current is $3A$ .
By Kirchhoff’s Law,
\[\frac{{\mathop V\nolimits_1 \mathop { + V}\nolimits_2 }}{{\mathop {R + r}\nolimits_1 \mathop { + r}\nolimits_2 }} = \mathop 3\nolimits_{} \]
Thus, we can say
$\mathop {(R + r}\nolimits_1 \mathop { + r}\nolimits_2 ) = \frac{{\mathop V\nolimits_1 \mathop { + V}\nolimits_2 }}{3} \cdot \cdot \cdot \cdot (1)$
Similarly for the second case when current is $1A$ ,
$\mathop V\nolimits_1 \mathop { - V}\nolimits_2 = \mathop {R + r}\nolimits_1 \mathop { + r}\nolimits_2 $
Now,
Putting in equation $(1)$, we get
$\mathop {3V}\nolimits_1 \mathop { - 3V}\nolimits_2 = \mathop V\nolimits_1 \mathop { + V}\nolimits_2 $
After further evaluation, we get
$\mathop {2V}\nolimits_1 = \mathop {4V}\nolimits_2 $
In the question, it is asked for $\frac{{\mathop V\nolimits_1 }}{{\mathop V\nolimits_2 }}$
Thus, we get
\[\frac{{\mathop V\nolimits_1 }}{{\mathop V\nolimits_2 }} = \frac{2}{1}\]
Hence, the answer is (B).
Additional Information: The Kirchhoff’s rules are handy to use in the cases for internal resistance, multiple $emf$ and in the cases indulging potentiometer. These rules are simple and very intuitive. Just that they were placed in a standardized manner by Kirchhoff.
The internal resistance we are talking about is referring to the resistance offered by the battery itself at initiation. This internal resistance value decides about the behavior of the circuit. Though minimal, but still of concern.
Note: We directly evaluated the result due to the application of the Kirchhoff’s law. One should not be confused about the direct relation. It is trivially coming from Kirchhoff's law.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)