Answer
427.8k+ views
Hint: We are given a circuit diagram with three resistors and two cells. Since the internal resistances of the cells are negligible we don’t need to consider them. By applying Kirchhoff’s loop rule and junction rule we will get two equations. By equating them we will obtain the current passing through each resistor. Using ohm’s law we will get the potential difference through the resistor.
Formula used:
Junction Rule, ${{I}_{in}}={{I}_{out}}$
Loop rule, $\sum{V}=0$
$V=IR$
Complete answer:
Consider the figure given below.
Let ‘$I$’ be the current flowing from the ‘$3V$’ battery.
We know that at the junction ‘C’ this current will split.
Therefore the current passing through the resistance $2k\Omega $ will be ‘${{I}_{1}}$’ and through the resistance $1k\Omega $ will be ‘${{I}_{2}}$ .
Then we know that according to Kirchhoff’s junction rule,
$I={{I}_{1}}+{{I}_{2}}$
Now let us consider the loop ABCFA in the given figure.
By applying Kirchhoff’s loop rule we will get,
$3-I-2{{I}_{1}}=0$
Since $I={{I}_{1}}+{{I}_{2}}$, we can write the above equation a,
\[\Rightarrow 3-\left( {{I}_{1}}+{{I}_{2}} \right)-2{{I}_{1}}=0\]
\[\Rightarrow 3-{{I}_{1}}-{{I}_{2}}-2{{I}_{1}}=0\]
By simplifying this we will get our first equation as,
\[\Rightarrow 3=3{{I}_{1}}+{{I}_{2}}\]
Let the above equation be the first equation.
Now let us consider the loop FCDEF in the given figure.
By applying Kirchhoff’s loop rule again, we will get
$2{{I}_{1}}-{{I}_{2}}-2=0$
By solving this we will get our second equation as,
$\Rightarrow 2=2{{I}_{1}}-{{I}_{2}}$
Now we have our first and second equation as,
\[3=3{{I}_{1}}+{{I}_{2}}\] and
$2=2{{I}_{1}}-{{I}_{2}}$
By comparing these two equations and adding them together, we get
$\Rightarrow 3{{I}_{1}}+{{I}_{2}}+2{{I}_{1}}-{{I}_{2}}=5$
$\Rightarrow 3{{I}_{1}}+2{{I}_{1}}=5$
$\Rightarrow 5{{I}_{1}}=5$
$\Rightarrow {{I}_{1}}=\dfrac{5}{5}=1mA$
Therefore the current passing through $2k\Omega $ resistor is $1mA$.
We need to find the potential difference across $2k\Omega $.
We know that by ohm’s law,
$V=IR$
Therefore the potential across $2k\Omega $ will be,
$\Rightarrow V=1mA\times 2k\Omega $
$\Rightarrow V=2V$
Hence the potential difference across $2k\Omega $ is $2V$.
Note:
Kirchhoff’s first rule is the junction rule. According to this rule the sum of all currents entering a junction will be always equal to the sum of all currents leaving the junction.
The second rule or the loop rule states that the sum of all the electric potential differences around a closed circuit or a loop is always zero.
Formula used:
Junction Rule, ${{I}_{in}}={{I}_{out}}$
Loop rule, $\sum{V}=0$
$V=IR$
Complete answer:
Consider the figure given below.
![seo images](https://www.vedantu.com/question-sets/bff93cc9-26ac-4a61-9dd2-40079f184fd24523804744045092505.png)
Let ‘$I$’ be the current flowing from the ‘$3V$’ battery.
We know that at the junction ‘C’ this current will split.
Therefore the current passing through the resistance $2k\Omega $ will be ‘${{I}_{1}}$’ and through the resistance $1k\Omega $ will be ‘${{I}_{2}}$ .
Then we know that according to Kirchhoff’s junction rule,
$I={{I}_{1}}+{{I}_{2}}$
Now let us consider the loop ABCFA in the given figure.
By applying Kirchhoff’s loop rule we will get,
$3-I-2{{I}_{1}}=0$
Since $I={{I}_{1}}+{{I}_{2}}$, we can write the above equation a,
\[\Rightarrow 3-\left( {{I}_{1}}+{{I}_{2}} \right)-2{{I}_{1}}=0\]
\[\Rightarrow 3-{{I}_{1}}-{{I}_{2}}-2{{I}_{1}}=0\]
By simplifying this we will get our first equation as,
\[\Rightarrow 3=3{{I}_{1}}+{{I}_{2}}\]
Let the above equation be the first equation.
Now let us consider the loop FCDEF in the given figure.
By applying Kirchhoff’s loop rule again, we will get
$2{{I}_{1}}-{{I}_{2}}-2=0$
By solving this we will get our second equation as,
$\Rightarrow 2=2{{I}_{1}}-{{I}_{2}}$
Now we have our first and second equation as,
\[3=3{{I}_{1}}+{{I}_{2}}\] and
$2=2{{I}_{1}}-{{I}_{2}}$
By comparing these two equations and adding them together, we get
$\Rightarrow 3{{I}_{1}}+{{I}_{2}}+2{{I}_{1}}-{{I}_{2}}=5$
$\Rightarrow 3{{I}_{1}}+2{{I}_{1}}=5$
$\Rightarrow 5{{I}_{1}}=5$
$\Rightarrow {{I}_{1}}=\dfrac{5}{5}=1mA$
Therefore the current passing through $2k\Omega $ resistor is $1mA$.
We need to find the potential difference across $2k\Omega $.
We know that by ohm’s law,
$V=IR$
Therefore the potential across $2k\Omega $ will be,
$\Rightarrow V=1mA\times 2k\Omega $
$\Rightarrow V=2V$
Hence the potential difference across $2k\Omega $ is $2V$.
Note:
Kirchhoff’s first rule is the junction rule. According to this rule the sum of all currents entering a junction will be always equal to the sum of all currents leaving the junction.
The second rule or the loop rule states that the sum of all the electric potential differences around a closed circuit or a loop is always zero.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![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)
How do you graph the function fx 4x class 9 maths 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)