Answer

Verified

54.9k+ views

**Hint:**In the given question, the circuit has two loops. We can apply Kirchhoff’s law for each loop to get the unknown current, voltage or resistance values by using the values given. We need to find the reading of the ammeter in a loop, so we will use the Kirchhoff’s second (voltage) law. As we know, Kirchhoff’s voltage law states that “The voltage around a loop is equal to the sum of every voltage drop in the same loop for any closed circuit”. We will use this law and form the equations for both loops separately and then we can solve the equations to get the value of the unknown parameter.

**Complete step by step solution:**

We will show the given circuit and name the different parameters in the diagram as shown below:

From the circuit, there are two loops i.e. ABCDEA and HCDFGH.

Now, to calculate the unknown parameters, we will use Kirchhoff's voltage law for both loops separately. We will calculate each voltage drop in a loop and put it equal to the voltage in the circuit.

For loop ABCDEA,

\[

\Rightarrow 2{i_1} + 2\left( {{i_1} + {i_2}} \right) = 2 \\

\Rightarrow 2{i_1} + 2{i_1} + 2{i_2} = 2 \\

\Rightarrow 4{i_1} + 2{i_2} = 2 \\

\Rightarrow 2{i_1} + 2{i_2} = 1...\left( 1 \right) \\

\]

For loop HCDFGH,

$

\Rightarrow 2\left( {{i_1} + {i_2}} \right) + 2{i_2} = 2 \\

\Rightarrow 2{i_1} + 2{i_2} + 2{i_2} = 2 \\

\Rightarrow 2{i_1} + 4{i_2} = 2 \\

\Rightarrow {i_1} + 2{i_2} = 1...\left( 2 \right) \\

$

From the equation (1) and (2),

$

\Rightarrow {i_1} + 2\left( {1 - 2{i_1}} \right) = 1 \\

\Rightarrow - 3{i_1} = - 1 \\

\Rightarrow {i_1} = \dfrac{1}{3}A \\

$

On solving,

$

\Rightarrow {i_2} = 1 - 2\left( {\dfrac{1}{3}} \right) \\

\Rightarrow {i_2} = \dfrac{1}{3}A \\

$

Thus, we can calculate the ammeter reading by adding the both currents.

$

i = {i_1} + {i_2} \\

\Rightarrow i = \dfrac{1}{3} + \dfrac{1}{3} \\

\Rightarrow i = \dfrac{2}{3}A \\

$

Therefore, the ammeter reading is $\dfrac{2}{3}A$ .

**Hence, the correct option is (C).**

**Note:**In the given question, we need to analyse the circuit and find the law which will help us to find the unknown parameter. For any circuit, we have to look for nodes or loops which are given. After that we can apply Kirchhoff's current law if nodes are given or Kirchhoff’s voltage law if loops are given. The equations for voltage drop and node current will lead us to find the required parameter.

Recently Updated Pages

Why do we see inverted images in a spoon class 10 physics JEE_Main

A farsighted man who has lost his spectacles reads class 10 physics JEE_Main

State whether true or false The outermost layer of class 10 physics JEE_Main

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Other Pages

Electric field due to uniformly charged sphere class 12 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main

In the ground state an element has 13 electrons in class 11 chemistry JEE_Main

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main