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?

Question

Quizplus · Accepted Answer

We can use the formula:

V = L di/dt

Where V is the voltage across the inductor, L is the inductance, and di/dt is the rate of change of current.

Since the current and voltage are given as amplitudes, we can use the RMS values, which are:

Irms = 200 mA / sqrt(2) = 141.4 mA

Vrms = 2.4 V / sqrt(2) = 1.7 V

At 1400 Hz, the angular frequency is:

ω = 2πf = 2π(1400) = 8800π rad/s

The derivative of the current waveform is:

di/dt = ω Irms cos(ωt + φ)

where φ is the phase angle between the current and voltage.

Since the current and voltage are in phase for an inductor, we have:

φ = 0

Therefore, di/dt = ω Irms = 8800π × 141.4×10^-3 = 1.24 A/s

Substituting these values into the formula, we get:

L = Vrms / di/dt = 1.7 / 1.24 = 1.37 mH

The closest answer choice to this value is B) 1.36 mH.

The Inductor in a Radio Receiver Carries a Current of Amplitude