Alternating Current

In the mechanical mass-spring analogy, the potential energy $\frac{1}{2}kx^2$ corresponds to which electrical energy?

If an LC circuit has $L = 1\,H$ and $\omega = 100\,rad/s$, what is the value of the capacitance $C$?

What is the value of the current in an LC circuit when the charge on the capacitor is zero?

The sum of electrostatic and magnetic energy in an ideal LC circuit is:

If the frequency of an LC circuit is $1\text{ MHz}$, and the inductance is $10\text{ \mu H}$, what is the approximate value of the capacitance?

The dimension of the term $1/(LC)$ is the same as that of:

In an LC circuit, the capacitor $C$ is charged to a maximum voltage $V_0$. The maximum value of $dI/dt$ is:

For an LC circuit, which of the following is a constant?

In an LC circuit, when the charge is $Q_0 / 2$, the ratio of the rate of change of magnetic energy to the rate of change of electric energy is:

A $10\text{ \mu F}$ capacitor is charged to $50\text{ V}$ and then connected to a $10\text{ mH}$ inductor. What is the frequency of the energy oscillations?

If the frequency of the AC source in a series LCR circuit is increased, the capacitive reactance ($X_C$) will:

What is the SI unit of the Quality factor ($Q$) of an LCR circuit?

Which component in an LCR circuit dissipates average power?

What happens to the impedance of a series LCR circuit at the resonant frequency?

What is the power dissipated in an LCR circuit at resonance if the peak voltage is $V_0$ and resistance is $R$?

A series LCR circuit has $L = 10\,mH$, $C = 1\,\mu F$, and $R = 10\,\Omega$. The bandwidth of the circuit is:

If the Q-factor of a circuit is high, it means:

In a specialized medical imaging device, an LCR series circuit is powered by an AC source $v = 283 \sin(314t) \text{ V}$. The components are $R = 3 \text{ \Omega}$, $L = 25.48 \text{ mH}$, and $C = 796 \text{ \mu F}$. Calculate the power factor of the circuit and determine if the current leads or lags the voltage.

In a series LCR circuit, if the potential differences are $V_R = 30\text{ V}$, $V_L = 60\text{ V}$, and $V_C = 20\text{ V}$, what is the phase angle between the current and the source voltage?

What is the relationship between the Quality factor $Q$ and the damping in an LCR circuit? High $Q$ indicates:

Selectivity of a series $LCR$ circuit is better if:

The $Q$-factor of an $LCR$ circuit is also equal to $\frac{\omega_r L}{R}$. This indicates that $Q$ is:

When $X_L = X_C$, the circuit is said to be in:

Which of the following is the unit of $1/\sqrt{LC}$?

A series $LCR$ circuit, as shown in the diagram, has a resonant angular frequency $\omega_0$ and a quality factor $Q$. If the resistance $R$, inductance $L$, and capacitance $C$ are all simultaneously doubled ($R \rightarrow 2R$, $L \rightarrow 2L$, $C \rightarrow 2C$), what will be the new resonant angular frequency $\omega'$ and the new quality factor $Q'$ of the circuit?

Which component in an $LCR$ circuit is responsible for the energy loss that determines the sharpness of the resonance?

A series $LCR$ circuit has a $Q$-factor of $5$. If the resonant frequency is $1000\text{ Hz}$, the bandwidth is:

A tuning circuit has an inductor of $1\ mH$ and a capacitor that can range from $10\ pF$ to $100\ pF$. What is the ratio of the maximum resonant frequency to the minimum resonant frequency?

If the current at resonance in a series $LCR$ circuit is $10\ A$ and the $Q$-factor is $50$, what is the current at the half-power frequencies?

At resonance, the reactive power in a series $LCR$ circuit is:

If an AC circuit has $V_{rms} = 100$ V, $I_{rms} = 2$ A, and the power dissipated is 100 W, the phase angle is:

What is the power factor when the reactance is equal to the resistance in a series circuit?

The average power dissipated in a cycle is given by $P = V_{rms} I_{rms} \cos \phi$. If the circuit contains only a resistor, then $\phi$ is:

Which of the following does NOT have a unit of Watt?

A $10 \Omega$ resistor is connected in series with an inductor of $10 \Omega$ reactance. The average power dissipated by the circuit when connected to a $100$ V RMS source is:

If the resistance in an AC circuit is zero, the power factor is:

As the frequency of an AC source increases, the power factor of a series RC circuit:

A $200 V$ AC source is connected to a device that consumes $1 kW$ of power. The voltage leads the current by $30^\circ$. If we represent the device as a series combination of a resistor and an inductor, find the value of the inductive reactance $X_L$.

A certain appliance is rated at $1100 W$ and $220 V$ AC. However, it has an inductive component such that the current lags the voltage by $\pi/3$. If the power company charges based on the RMS current drawn, and you want to reduce the current to the minimum possible value while maintaining the same real power $P$, what is the ratio of the new current to the old current?

In a radio receiver circuit (LCR series), the Q-factor is 100 and the resonant frequency is $1 MHz$. If the power dissipated at resonance is $10 W$ for a source voltage of $10 V$, what is the power dissipated when the source frequency is adjusted to $1.005 MHz$?

If the number of turns in the primary coil is doubled while keeping other factors constant, the secondary voltage will:

Which loss occurs because the iron core itself acts as a conductor in a changing magnetic field?

The magnetic core of a transformer is usually:

A device that increases the voltage level of an AC signal while decreasing its current level is a:

In a transformer, the primary coil has $N_p$ turns and the secondary has $N_s$ turns. If a load of resistance $R$ is connected to the secondary, the equivalent resistance 'seen' by the primary source is:

Which of the following statements about an ideal transformer is true?

Large transformers are often submerged in oil. The primary purpose of this oil is:

A transformer has an efficiency of $80\%$ and works at $100 \text{ V}$ and $4 \text{ kW}$. If the secondary voltage is $200 \text{ V}$, calculate the primary and secondary currents.

If the primary of a transformer is energized by a square wave voltage, the flux waveform in the core will be:

The voltage regulation of a transformer at unity power factor is generally:

If the AC voltage is $V = V_0 \sin(\omega t)$, then for a pure resistor the current is:

The relation between frequency $f$ and time period $T$ is:

The reactance of an inductor ______ as the frequency of AC increases.

The reactance of a capacitor ______ as the frequency of AC increases.

A $10 \mu F$ capacitor is charged to $100 \text{ V}$ and then connected to an AC source of $100 \text{ V}$ RMS. The capacitor:

In an AC circuit, the instantaneous values of voltage and current are $V = V_0 \sin \omega t$ and $I = I_0 \sin(\omega t - \pi/2)$. The average power dissipated is:

If $V = 100 \sin(100t)$ and $I = 2 \sin(100t + \pi/2)$, the circuit element is:

An AC voltage $v = 100 \sin(314 t)$ is applied to a resistor of $50 \Omega$. The RMS current is:

Which of the following is true for a pure inductor in an AC circuit?

When a capacitor is connected to a DC source, its reactance is:

A phasor diagram can represent multiple AC voltages only if they all have the same:

At resonance in a series LCR circuit, the phasors $V_L$ and $V_C$:

If the current phasor leads the voltage phasor by $\pi/2$, the circuit component is:

Which component does the phrase 'current lags voltage' refer to in a phasor diagram?

A phasor diagram represents the state of an AC circuit at a specific instant. If we 'freeze' the rotation at $t = T/4$ (where $T$ is the period), a phasor representing $\sin(\omega t)$ will be pointing along the:

In a series LCR circuit, the angle $\phi$ by which the voltage leads the current is given by $\tan \phi = (X_L - X_C)/R$. If $X_L = 20 \Omega, X_C = 10 \Omega, R = 10 \Omega$, then $\phi$ is:

Which physical quantity is conserved when we add two AC voltages using the phasor method?

At resonance in a series LCR circuit, the phasor representing the voltage across the inductor and the phasor representing the voltage across the capacitor:

In a phasor diagram, the instantaneous voltage is the vertical projection. If the voltage is $v = V_m \cos(\omega t)$, the phasor at $t=0$ must be at which angle with respect to the positive x-axis?

For a series LCR circuit, as the frequency $\omega$ approaches infinity, what happens to the orientation of the total voltage phasor $\vec{V}$ relative to the current phasor $\vec{I}$?