A.C Fundamentals, Circuits And Circuit Theory MCQ Questions & Answers | Electrical Engineering

Resonant Frequency: The resonant frequency of a coil in an AC circuit is determined by both its inductance and capacitance. It is given by the formula:

$$f_r = \frac{1}{2 \pi \sqrt{L C}}$$

where $$f_r$$ is the resonant frequency, L is the inductance, and C is the capacitance.

Effect of Capacitance: From the formula, it is clear that the resonant frequency is inversely proportional to the square root of the capacitance. Therefore, a lower capacitance results in a higher resonant frequency.

Options Analysis:

Option A: A coil with large resistance - The resistance of the coil does not directly affect the resonant frequency.

Option B: A coil with low resistance - Similar to option A, resistance does not directly impact the resonant frequency.

Option C: A coil with large distributed capacitance - Larger capacitance results in a lower resonant frequency.

Option D: A coil with low distributed capacitance - Lower capacitance results in a higher resonant frequency.

Therefore, the coil with low distributed capacitance will have a large resonant frequency.

The correct answer is Option C: Square wave
Let's break down why:

Understanding RMS and Mean Values:
* RMS Value (Root Mean Square): It's the effective value of a waveform. Think of it as the DC equivalent that would produce the same heating effect in a resistor.
* Mean Value (Average Value): It's the average value of the waveform over one complete cycle.

Why Square Wave?
A square wave spends equal time at its positive peak and its negative peak (or zero, depending on the type).
* RMS: Since the power dissipated is the same whether the voltage is positive or negative (because power is proportional to voltage squared), the RMS value is simply the amplitude of the square wave.
* Mean: If the square wave alternates between a positive value (+V) and a negative value (-V) the mean value over a complete cycle is zero. If it alternates between a positive value (+V) and zero (0), the mean value is V/2. However, if we consider only the magnitude (absolute value) of the waveform, then the mean value becomes equal to the amplitude (+V). Therefore RMS is equal to the average.

Why Not the Other Options?
* Triangular Wave: The RMS and mean values are different because the waveform changes linearly, not abruptly.
* Sine Wave: The RMS value is Vm/√2 (where Vm is the peak value) and the mean value over a full cycle is zero. Mean value is zero but average value can be calculated over half a cycle.
* Half-Wave Rectified Sine Wave: Only the positive (or negative) half of the sine wave is present. The RMS and mean values are different because the waveform is not symmetrical around zero and includes a significant period of zero voltage.