# What is the impedance of the circuit shown in the figure given below?

A. $100\,ohm$

B. $50\,ohm$

C. $30\,ohm$

D. $40\,ohm$

Answer

Verified

279.3k+ views

**Hint:**Impedance is the net resistance of ac circuits when inductors, capacitors and resistors are used in a circuit. We will find the value of resistance of resistor and inductor separately and then using the formula of finding impedance which is given as $Z = \sqrt {{{({X_L})}^2} + {R^2}} $.

**Complete step by step answer:**

Let us first understand the impedance formula. Impedance is denoted by $Z$ and resistance of an inductor is given by ${X_L} = \dfrac{V}{I}$ since, voltage across the inductor is given in figure as ${V_{inductor}} = 120V$ . And since, current is flowing in the circuit which is given by, $I = 3A$ .

Since, both resistor and inductor are connected in series, and we also know in series circuits current flows equally in all components of circuit which means the same current $I = 3A$ will flow in both resistor and inductor. Now, the value of resistance in inductor is given by:

${X_L} = \dfrac{V}{I}$

$\Rightarrow {X_L} = \dfrac{{120}}{3}$

$\Rightarrow {X_L} = 40\,ohm \to (i)$

Now, we will find the magnitude of resistance across the resistor.

From given figure, voltage across the resistor is $90V$

$R = \dfrac{V}{I}$

$\Rightarrow R = \dfrac{{90}}{3}$

$\Rightarrow R = 30\,ohm \to (ii)$

From equations $(i)and(ii)$ we get the value of impedance as

$Z = \sqrt {{{({X_L})}^2} + {R^2}} $

Putting the values from $(i)and(ii)$ ,

$Z = \sqrt {1600 + 900} $

$\Rightarrow Z = \sqrt {2500} $

$\therefore Z = 50\,ohm$

So, the net resistance which is known as impedance is $Z = 50\,ohm$.

**Hence, the correct option is B.**

**Note:**Remember, in electrical circuit when inductor and resistor are connected in series then they are in phase difference of ${90^ \circ }$ where current lags behind the voltage by ${90^ \circ }$ and so their net impedance term of $\cos \phi $ became zero since $\cos {90^ \circ } = 0$ hence, impedance is simply the root of sum of squares of inductance and resistance.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What are the measures one has to take to prevent contracting class 12 biology CBSE

Suggest some methods to assist infertile couples to class 12 biology CBSE

Trending doubts

What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the past tense of read class 10 english CBSE

What is pollution? How many types of pollution? Define it

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

How many crores make 10 million class 7 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE