Answer
64.8k+ views
Hint: The impedance of the circuit is determined by using the impedance of the circuit formula, by using this formula and also by using the values of the inductive reactance, capacitive reactance and the resistance values, then the impedance in the circuit can be determined.
Formula used:
The impedance of the circuit is given by,
$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} $
Where, $Z$ is the impedance of the circuit, ${X_L}$ is the inductive reactance of the circuit, ${X_C}$ is the capacitive reactance of the circuit and $R$ is the resistance of the circuit.
Complete step by step solution:
Given that,
The inductive reactance of the circuit is, ${X_L} = 8\,\Omega $
The capacitive reactance of the circuit is, ${X_C} = 6\,\Omega $
The resistance of the circuit is, $R = 10\,\Omega $
Now,
The impedance of the circuit is given by,
$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} \,................\left( 1 \right)$
By substituting the inductive reactance of the circuit, the capacitive reactance of the circuit and the resistance of the circuit in the above equation (1), then the above equation (1) is written as,
$Z = \sqrt {{{10}^2} + {{\left( {8 - 6} \right)}^2}} $
By subtracting the terms in the above equation, then the above equation is written as,
$Z = \sqrt {{{10}^2} + {2^2}} $
By squaring the terms inside the square root in the above equation, then the above equation is written as,
$Z = \sqrt {100 + 4} $
By adding the terms inside the square root in the above equation, then the above equation is written as,
$Z = \sqrt {104} $
By taking the square root in the above equation, then the above equation is written as,
$Z = 10.19\,\Omega $
Then the above equation is approximately written as,
$Z \simeq 10.2\,\Omega $
Hence, the option (A) is the correct answer.
Note: The impedance of the circuit is dependent only on the resistance of the circuit, the inductive reactance of the circuit, the capacitive reactance of the circuit. The impedance is also the form of the resistance and it is the measure of the overall opposition of the current in the circuit.
Formula used:
The impedance of the circuit is given by,
$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} $
Where, $Z$ is the impedance of the circuit, ${X_L}$ is the inductive reactance of the circuit, ${X_C}$ is the capacitive reactance of the circuit and $R$ is the resistance of the circuit.
Complete step by step solution:
Given that,
The inductive reactance of the circuit is, ${X_L} = 8\,\Omega $
The capacitive reactance of the circuit is, ${X_C} = 6\,\Omega $
The resistance of the circuit is, $R = 10\,\Omega $
Now,
The impedance of the circuit is given by,
$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} \,................\left( 1 \right)$
By substituting the inductive reactance of the circuit, the capacitive reactance of the circuit and the resistance of the circuit in the above equation (1), then the above equation (1) is written as,
$Z = \sqrt {{{10}^2} + {{\left( {8 - 6} \right)}^2}} $
By subtracting the terms in the above equation, then the above equation is written as,
$Z = \sqrt {{{10}^2} + {2^2}} $
By squaring the terms inside the square root in the above equation, then the above equation is written as,
$Z = \sqrt {100 + 4} $
By adding the terms inside the square root in the above equation, then the above equation is written as,
$Z = \sqrt {104} $
By taking the square root in the above equation, then the above equation is written as,
$Z = 10.19\,\Omega $
Then the above equation is approximately written as,
$Z \simeq 10.2\,\Omega $
Hence, the option (A) is the correct answer.
Note: The impedance of the circuit is dependent only on the resistance of the circuit, the inductive reactance of the circuit, the capacitive reactance of the circuit. The impedance is also the form of the resistance and it is the measure of the overall opposition of the current in the circuit.
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)