Question 253: AC fundamentals

Question

An a.c. source of frequency ' f ' is connected to a circuit containing an inductance ' $L$ ' and resistance ' R ' in series. The impedance of this circuit is

Accepted Answer

Step 1: Recall impedance in an $R-L$ circuit
For a resistor $R$ (resistance) in series with an inductor $L$, the impedance is given by
$ Z = \sqrt{R^2 + X_L^2} $
where $X_L$ is the inductive reactance.
Step 2: Inductive reactance
The inductive reactance is:
$ X_L = \omega L = 2 \pi f L $
Step 3: Substitute
So,
$ Z = \sqrt{R^2 + (2\pi f L)^2} $
Step 4: Compare with options
Option D:
$ \sqrt{R^2 + 4 \pi^2 f^2 L^2} $
matches perfectly.
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Correct Answer: Option D

Answer

$\sqrt{\mathrm{R}^2+2 \pi \mathrm{fL}^2}$

Answer

$\sqrt{\mathrm{R}^2+\mathrm{L}^2}$

Answer

$\mathrm{R}+2 \pi \mathrm{fL}$

Answer

$\sqrt{\mathrm{R}^2+4 \pi^2 \mathrm{f}^2 \mathrm{~L}^2}$

AC fundamentals

An a.c. source of frequency ' f ' is connected to a circuit containing an inductance ' L ' and resistance ' R ' in series. The impedance of this circuit is

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