Practice Questions

Define alternating current (AC).

Recall the relationship between the peak value ($i_m$) and the root mean square (rms) value ($I$) of an alternating current.

Name the physical quantity that plays the role of resistance in a purely inductive AC circuit and state its SI unit.

Examine the main reason why alternating current (AC) is preferred over direct current (DC) for the large-scale transmission of electrical energy.

An AC voltage source is described by the equation $v = 150 \sin(100\pi t)$. If this source is connected to a $50 \text{ } \Omega$ resistor, calculate the rms value of the current flowing through the resistor.

Define the power factor of an AC circuit.

Evaluate the necessity of using a laminated iron core in a transformer instead of a solid iron core.

An ideal step-down transformer is used to power a $12$ V lamp from a $240$ V mains supply. If the lamp draws a current of $2$ A, calculate the current drawn from the mains. Assume the transformer is 100% efficient.

Critique the use of the term 'wattless current'. Is the current truly 'wattless', and under what specific conditions is this term applicable?

The peak voltage of an AC supply is measured to be $340$ V. Calculate its rms voltage.

A capacitor of capacitance $100 \text{ } \mu F$ is connected to an AC supply of $110$ V, $60$ Hz. Calculate the capacitive reactance and the peak current in the circuit.

Compare the phase relationship between voltage and current in a purely resistive, a purely inductive, and a purely capacitive AC circuit. Demonstrate these relationships using phasor diagrams.

Examine why the average power consumed by a pure inductor or a pure capacitor in an AC circuit over one complete cycle is zero.

Explain why AC voltage is preferred over DC voltage for long-distance transmission of electrical energy.

Identify the circuit elements in which the average power consumed over a complete AC cycle is zero.

Recall the formula for capacitive reactance ($X_C$) and explain how it depends on the frequency of the AC source.

For a series LCR circuit with $L = 2.0$ H, $C = 32 \text{ } \mu F$, and $R = 10 \text{ } \Omega$, calculate the resonant frequency. Also, solve for the impedance and the rms current at the resonant frequency if the circuit is connected to a $220$ V AC source.

Define impedance in a series LCR circuit and recall its formula.

A household AC supply is rated at $220 \text{ V}$. Explain what this value represents and calculate the peak voltage of the source.

Define wattless current.

List three types of energy losses that occur in an actual transformer.

Describe what a step-down transformer does and explain the relationship between the number of turns in its primary and secondary coils.

A pure inductor with an inductance of $50$ mH is connected to an AC source of $220$ V, $50$ Hz. Calculate the inductive reactance and the rms current in the circuit.

Analyze how the inductive reactance ($X_L$) and capacitive reactance ($X_C$) of a circuit change with the frequency of the AC source. Contrast their behavior.

A light bulb is connected in series with an inductor to an AC source. Analyze what happens to the brightness of the bulb when the frequency of the AC source is increased, and explain your reasoning.

In a purely inductive circuit, the average power consumed over a complete cycle is zero. Justify this statement using both a mathematical derivation and a conceptual explanation.

Critique the statement: 'In a series LCR circuit at resonance, the individual voltages across the inductor and capacitor can be much larger than the source voltage, which violates the law of conservation of energy.'

A student designs a step-up transformer with $N_p = 50$ turns and $N_s = 500$ turns. They expect a 10x voltage increase. However, upon testing, they observe significant heating in the iron core and the output voltage is lower than expected. Justify the possible reasons for these discrepancies from the ideal transformer model.

Evaluate the claim that transmitting electrical power over long distances using low-voltage DC is more efficient than using high-voltage AC. Provide a reasoned argument to support or refute this claim.

Propose a method to determine whether an unknown circuit element in a sealed box is a resistor, an inductor, or a capacitor, using only a variable frequency AC voltage source and an AC ammeter.

An iron-core inductor is connected in series with a light bulb to an AC source. Justify what happens to the brightness of the bulb when the frequency of the AC source is increased. How would your answer change if the inductor were replaced by a capacitor?

Design a simple series LCR circuit that would resonate at a frequency of $1000$ Hz. Propose specific values for L and C, and justify why your chosen values are practical for a laboratory setup. Also, evaluate the effect of adding a resistor with a high resistance value on the sharpness of resonance.

Create a hypothetical scenario for an engineer designing a power supply for a sensitive electronic device that requires a low DC voltage from a standard high-voltage AC main. Propose a block diagram of the system they would need to build, justifying the function of each component, especially the transformer and a capacitor.

Propose a modification to a series LCR circuit, initially operating at a frequency below its resonance, to bring it into resonance without changing the source frequency. Justify two distinct methods to achieve this.

Formulate a problem involving a series LCR circuit where the power factor is $0.5$ (lagging). The circuit is connected to a $240 \text{ V}$, $50 \text{ Hz}$ source, and has a resistance of $R = 30 \Omega$. Propose values for L and C that satisfy these conditions and then calculate the total impedance and the average power dissipated.

Design an experiment to verify the phase relationship between voltage and current in a purely capacitive AC circuit. Your design should include a circuit diagram, the equipment needed, the procedure, and a description of the expected output on a Cathode Ray Oscilloscope (CRO).

Evaluate the role of the power factor in industrial electricity billing. Why do power companies penalize industrial consumers with low power factors, and how can these consumers improve their power factor? Justify your answer.

In a series LCR circuit, $R = 300 \text{ } \Omega$, $L = 0.9$ H, $C = 2.0 \text{ } \mu F$, and the source is $V = 150$ V with angular frequency $\omega = 1000$ rad/s. Calculate the power factor and the average power dissipated in the circuit.

A $10 \text{ } \mu F$ capacitor and a $50 \text{ } \Omega$ resistor are connected in series to a $110$ V, $50$ Hz AC source. Calculate the rms current in the circuit. Also, calculate the rms voltage across the resistor and the capacitor. Demonstrate why the algebraic sum of these voltages is not equal to the source voltage.

Analyze how connecting a capacitor of an appropriate value in parallel can improve the power factor of an inductive circuit where the current lags the voltage.

Explain the phenomenon of resonance in a series LCR circuit. State the condition for resonance and recall the formula for the resonant frequency.

A series LCR circuit has $R = 10 \text{ } \Omega$, $L = 80$ mH, and $C = 50 \text{ } \mu F$. It is connected to a variable frequency $200$ V AC source. Calculate the impedance of the circuit and the amplitude of the current when the angular frequency of the source is $200 \text{ rad/s}$.

Explain the function of a phasor in the analysis of AC circuits. Describe how phasors are used to represent AC voltage and current.

Formulate a mathematical expression for the quality factor (Q-factor) of a series LCR circuit and justify its significance. Design a scenario where a high Q-factor is desirable and another where a low Q-factor is preferred.

Summarize the phase relationship between the applied AC voltage and the resulting current in a purely resistive, a purely inductive, and a purely capacitive circuit.