Question

The inductor in a radio receiver carries a current of amplitude 200 mA when a voltage of amplitude 2.4 V is across it at a frequency of 1400 Hz. What is the value of the inductance

Answer 1

Answer:

The value of the inductance is 1.364 mH.

Explanation:

Given;

amplitude current, I₀ = 200 mA = 0.2 A

amplitude voltage, V₀ = 2.4 V

frequency of the wave, f = 1400 Hz

The inductive reactance is calculated;

$X_l = \frac{V_o}{I_o} \\\\X_l = \frac{2.4}{0.2} \\\\X_l =12 \ ohms$

The inductive reactance is calculated as;

$X_l = \omega L\\\\X_l = 2\pi fL\\\\L = \frac{X_l}{2 \pi f}$

where;

L is the inductance

$L = \frac{12}{2 \pi \times \ 1400} \\\\L = 1.364 \times \ 10^{-3} \ H\\\\L = 1.364 \ mH$

Therefore, the value of the inductance is 1.364 mH.

Answer 2

The value of inductance will be "1.36 mH".

Given values are:

• Current, $I_0 = 200 \ mA, or \ 0.2 \ A$
• Voltage, $V_0 = 2.4 \ V$
• Frequency, $f = 1400 \ Hz$

As we know the formula,

→ $X_l = \frac{V_0}{I_0}$

By substituting the values, we get

       $= \frac{2.4}{0.2}$

       $= 12 \ ohms$

Now,

The inductive reactance will be:

→ $X_l = \omega L$

or,

→ $X_l = 2 \pi f L$

Hence,

The Inductance will be:

→ $L = \frac{X_i}{2 \pi f}$

By putting the values, we get

      $= \frac{12}{2 \pi\times 1400}$

      $= 1.364\times 10^{-3} \ H$

      $= 1.36 \ mH$

Thus the above answer is right.

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