FIGURE Q32.1 shows emf phasors 1, 2, and 3.

1. For each, what is the instantaneous value of the emf?

2. At this instant, is the magnitude of each emf increasing, decreasing, or holding constant?

FIGURE Q32.1

A resistor is connected across an oscillating emf. The peak current through the resistor is 2.0 A. What is the peak current if:

1. The resistance $R$ is doubled?

2. The peak emf ${\epsilon }_{\text{}0}$ is doubled?

3. The frequency $\omega$ is doubled?

A capacitor is connected across an oscillating emf. The peak current through the capacitor is 2.0 A. What is the peak current if:

1. The capacitance $C$ is doubled?

2. The peak emf ${\epsilon }_{\text{}0}$ is doubled?

3. The frequency $\omega$ is doubled?

A low-pass $RC$ filter has a crossover frequency $f_{\text{c}}=200\text{Hz}$. What is $f_{\text{c}}$ if:

1. The resistance $R$ is doubled?

2. The capacitance $C$ is doubled?

3. The peak emf ${\epsilon }_{\text{}0}$ is doubled?

An inductor is connected across an oscillating emf. The peak current through the inductor is 2.0 A. What is the peak current if:

1. The inductance $L$ is doubled?

2. The peak emf ${\epsilon }_{\text{}0}$ is doubled?

3. The frequency $\omega$ is doubled?

The resonance frequency of a series $RLC$ circuit is 1000 Hz. What is the resonance frequency if:

1. The resistance $R$ is doubled?

2. The inductance $L$ is doubled?

3. The capacitance $C$ is doubled?

4. The peak emf ${\epsilon }_{\text{}0}$ is doubled?

In the series $RLC$ circuit represented by the phasors of FIGURE Q32.7, is the emf frequency less than, equal to, or greater than the resonance frequency ${\omega }_0?$ Explain.

FIGURE Q32.7

The resonance frequency of a series $RLC$ circuit is less than the emf frequency. Does the current lead or lag the emf? Explain.

The current in a series $RLC$ circuit lags the emf by $20\text{°}$. You cannot change the emf. What two different things could you do to the circuit that would increase the power delivered to the circuit by the emf?

The average power dissipated by a resistor is 4.0 W. What is $P_{\text{R}}$ if:

1. The resistance $R$ is doubled while ${\epsilon }_{\text{}0}$ is held fixed?

2. The peak emf ${\epsilon }_{\text{}0}$ is doubled while $R$ is held fixed?

3. Both are doubled simultaneously?