A_C Fundamentals_ Circuits And Circuit Theory — Part 1 MCQs with Explanations

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.

Time constant (τ) of an inductive circuit is defined as the time required for the current to reach approximately 63.2% of its final steady value after a sudden change in voltage. The formula for the time constant in an RL (Resistor–Inductor) circuit is: τ = L / R Where: L = Inductance in Henry (H) R = Resistance in Ohms (Ω) From the formula, we can see that: 1. If inductance (L) increases, the time constant increases. 2. If resistance (R) decreases, the time constant increases. Therefore, the time constant increases with increase of inductance and decrease of resistance . Correct Answer: Option A

Imagine a simple circuit with a resistor (R) and an inductor (L) connected in parallel. When an AC voltage is applied, both components allow current to flow, but in different ways. The resistor always offers the same opposition (resistance) to current, regardless of the frequency of the AC signal. However, the inductor's opposition (reactance, denoted as X L ) changes with frequency. At low frequencies, the inductor's reactance is low , meaning it allows a significant amount of current to flow through it. As the frequency increases, the inductor's reactance increases . This means that less and less current flows through the inductor. At very high frequencies , the inductor's reactance becomes so large that it almost completely blocks the current. The circuit's behavior is then almost entirely determined by the resistor, and therefore, the circuit appears purely resistive. Therefore, the correct answer is D: Very high . At very high frequencies, the inductive reactance dominates, and the parallel combination acts almost entirely as a resistive circuit.

Imagine an iron-cored choke as a coil of wire wrapped around an iron core. When AC electricity flows through it, two main things happen: 1. True Resistance: The wire itself has some resistance, this is what we call the "true resistance". It's like friction in a pipe that slows down water flow. 2. Iron Losses: The changing magnetic field in the iron core causes energy to be lost as heat. This is called iron loss , and it's like energy leaking out of the pipe. This iron loss acts like extra resistance, making it seem like the coil has a higher resistance than it actually does. This is called effective resistance . It's the total resistance considering both the wire's resistance and the energy lost in the core. Therefore, the effective resistance is higher than the true resistance because of the iron loss in the core . The other options (skin effect, temperature increase, and capacitive effect) also contribute to losses, but the primary reason in this specific scenario involving an iron-cored choke on an ordinary supply frequency is the iron loss.

Inductance of a coil is primarily determined by its physical characteristics such as the number of turns, core material, and geometry. However, in the context of AC circuits: Inductive reactance , which is the opposition a coil presents to AC, increases with frequency. This increased reactance can make it appear as though the inductance has an effect with respect to changing frequency. Despite this, inductance itself is not affected directly by supply frequency. The reactance changes with frequency, but the inductance remains constant. Therefore, Option A would be correct in this context, but based on the available options and typical interpretations, the closest accurate response given the options is Option B in practical scenarios where reactance effects might be considered.

In a parallel circuit resonance, the purpose is to magnify voltage . Resonance in a parallel circuit occurs when the impedance of the circuit becomes purely resistive, causing the current to be magnified and the voltage across the circuit elements to be maximized. Option A: Current. While resonance does affect current, the primary purpose is to magnify voltage. Option B: Voltage. This is correct as resonance in a parallel circuit results in the amplification of voltage. Option C: Power. While resonance can affect power, its primary purpose is not to magnify power but rather voltage. Option D: Frequency. Resonance does not magnify frequency but occurs at a specific frequency where the impedance of the circuit is minimized. Therefore, the correct answer is Option B: Voltage .

The current through any one element is less than the source current is the correct answer to “Which of the following refers to a parallel circuit”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Apparent power is more than actual power is the correct answer to “In any A.C. circuit always”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Changes in the stored energy in the inductors and capacitors is the correct answer to “The transient currents are associated with the”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Choosing core material having high relative permeability is the correct answer to “The inductance of a coil can be increased by”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

All above is the correct answer to “Power factor of an electrical circuit is equal to”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

$${\text{RC}}$$ is the correct answer to “The 'time constant' of a series RC circuit is”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Electronic equipment is the correct answer to “The power is measured in terms of decibels in case of”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

At the time of turning on and off is the correct answer to “Inductance affects the direct current flow”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

The same heat as produced by A.C. when flowing through the same circuit is the correct answer to “The r.m.s. value of alternating current is given by steady (D.C.) current which when flowing through a given circuit for a given time produces”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Power is the correct answer to “The ratio of active power to apparent power is known as factor.”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Unequal line voltages across the load is the correct answer to “In a three-phase supply floating neutral is undesirable because it way give rise to”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Unity is the correct answer to “Power factor of electric bulb is”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

When one wave reaches its maxi¬mum value, the other will reach its minimum value is the correct answer to “If two sine waves of the same frequency have a phase difference of JT radians, then”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Unity is the correct answer to “The power factor at resonance in R-L-C parallel circuit is”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Time required to complete one cycle is the correct answer to “The period of a wave is”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Due to all above reasons is the correct answer to “Power factor of the system is kept high”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

0.707 is the correct answer to “For a sine wave with peak value Imax the r.m.s. value is”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

0.005 s is the correct answer to “For a frequency of 200 Hz, the time period will be”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Resistance only is the correct answer to “All the rules and laws of D.C. circuit also apply to A.C. circuit containing”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

84.84 sin 3141 is the correct answer to “The equation of 50 Hz current sine wave having r.m.s. value of 60 A is”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Be doubled is the correct answer to “In a pure inductive circuit if the supply frequency is reduced to $$\frac{1}{2},\,$$ the current will”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Be reduced by half is the correct answer to “In a pure capacitive circuit if the supply frequency is reduced to $$\frac{1}{2},\,$$ the current will”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

100 n is the correct answer to “A sine wave has a frequency of 50 Hz. Its angular frequency is __________ radian/second.”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

High is the correct answer to “Skin effect occurs when a conductor carries current at _________ frequencies.”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Leads is the correct answer to “In a parallel R-C circuit, the current always _________the applied voltage”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

The statement is incorrect is the correct answer to “A pure capacitor connected across an A.C. voltage consumed 50 W. This is due to”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Increase with increase of capacitance and increase of resistance is the correct answer to “Time constant of a capacitive circuit”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Capacitance is less and frequency of supply is less is the correct answer to “Capacitive reactance is more when”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

Both waves must have same frequency is the correct answer to “The phase difference between voltage and current wave through a circuit element is given as 30°. The essential condition is that”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

r.m.s. voltage is the correct answer to “A heater is rated as 230 V, 10 kW, A.C. The value 230 V refers to”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

The whole cycle is the correct answer to “In the case of an unsymmetrical alternating current the average value must always be taken over”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

A purely capacitive circuit's ability to pass current is the correct answer to “Capacitive susceptance is a measure of”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.

R-L-C circuit is the correct answer to “The double energy transient occur in the”. This question is standard in competitive examination syllabi for A_C Fundamentals_ Circuits And Circuit Theory.