Answer
385.5k+ views
Hint: In order to answer the given question we need to apply the voltage-current relation from Ohm’s law in the given circuit. Also, we need to apply Kirchhoff’s law to the loops in the given circuit. After that we need to solve the obtained equations and finally conclude with the solution of the given question. Therefore, we need to solve the equation formed to conclude with the solution.
Complete step by step answer:
Let us redraw the circuit and name the loops in the given circuit.
Also let us assume that current $ {I_1} $ is flowing through the $ 10\Omega $ resistor.
And current flowing through $ {P_2}B $ be $ I - {I_1} $
Now we need to apply KVL to the closed loop $ A{P_2}{P_1}CA $
$ - 10{I_1} - 2I + 5 = 0 $
$ \Rightarrow 2I + 10{I_1} = 5............(i) $
Similarly by applying KVL to the closed loop $ {P_2}BD{P_1}{P_2} $ , we get,
$ 2 - 1(I - {I_1}) + 10y = 0 $
$ \Rightarrow I - 11{I_1} = 2...........(ii) $
Now on multiplying equation (ii) by $ 2 $ we get,
$ 2I - 22{I_1} = 4 $ …………..(iii)
Step four
Now, we need to subtract equation (iii) from equation (i)
By doing so, we get,
$ 32{I_1} = 1 $
$ \Rightarrow {I_1} = \dfrac{1}{{32}} = 0.031A $
Therefore, the required amount of current that is flowing through the $ 10\Omega $ resistance is $ 0.031A $ .
Hence, the correct answer is option (C).
Note: There are two rules according to Kirchhoff’s law. One is Kirchhoff voltage law (KVL) and the other is Kirchhoff’s current law (KCL). According to KVL the sum of all the potential in a closed loop is zero. Similarly according to KCL the sum of all the current in a closed loop is zero. Both KVL and KCL follow the conservation of energy across a closed loop or path.
Complete step by step answer:
Let us redraw the circuit and name the loops in the given circuit.
Also let us assume that current $ {I_1} $ is flowing through the $ 10\Omega $ resistor.
And current flowing through $ {P_2}B $ be $ I - {I_1} $
Now we need to apply KVL to the closed loop $ A{P_2}{P_1}CA $
$ - 10{I_1} - 2I + 5 = 0 $
$ \Rightarrow 2I + 10{I_1} = 5............(i) $
Similarly by applying KVL to the closed loop $ {P_2}BD{P_1}{P_2} $ , we get,
$ 2 - 1(I - {I_1}) + 10y = 0 $
$ \Rightarrow I - 11{I_1} = 2...........(ii) $
Now on multiplying equation (ii) by $ 2 $ we get,
$ 2I - 22{I_1} = 4 $ …………..(iii)
Step four
Now, we need to subtract equation (iii) from equation (i)
By doing so, we get,
$ 32{I_1} = 1 $
$ \Rightarrow {I_1} = \dfrac{1}{{32}} = 0.031A $
Therefore, the required amount of current that is flowing through the $ 10\Omega $ resistance is $ 0.031A $ .
Hence, the correct answer is option (C).
Note: There are two rules according to Kirchhoff’s law. One is Kirchhoff voltage law (KVL) and the other is Kirchhoff’s current law (KCL). According to KVL the sum of all the potential in a closed loop is zero. Similarly according to KCL the sum of all the current in a closed loop is zero. Both KVL and KCL follow the conservation of energy across a closed loop or path.
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)