91Ó°ÊÓ

The emf phasor in FIGURE EX32 .1 is shown at$t=2.0ms$.

a. What is the angular frequency $\mathrm{Ó\neg }$? Assume this is the first rotation.

b. What is the peak value of the emf?

FIGURE $Q32.1$shows emf phasors a, b, and c.

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

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

a. Evaluate $V_R$ in figure at emf frequencies$100,300,1000,3000,10000Hz$

b. Graph $V_R$versus frequency. Draw a smooth curve through your five points.

What are$V_{\mathrm{R}}$and $V_{\mathrm{C}}$if the emf frequency in FIGURE is $10\mathrm{kHz}$?

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

a. The resistance $R$is doubled?

b. The peak emf $E0$is doubled?

c. The frequency $v$is doubled?

The emf phasor in FIGURE EX32.2 is shown at $t=15ms$.

a. What is the angular frequency $\mathrm{Ó\neg }$? Assume this is the first rotation.

b. What is the instantaneous value of the emf?

The peak current through an inductor is $10mA$. What is the peak current if

a. The emf frequency is doubled?

b. The emf peak voltage is doubled (at the original frequency)

FIGURE EX32.24 shows voltage and current graphs for an inductor.

a. What is the emf frequency $f$?

b. What is the value of the inductance $L$?

A series RLC circuit has a $200kHz$ resonance frequency. What is the resonance frequency if

a. The resistor value is doubled?

b. The capacitor value is doubled?

A capacitor is connected across an oscillating emf. The peak current through the capacitor is $2A .$What is the peak current if:

a. The capacitance $C$is doubled?

b. The peak emf $E0$is doubled?

c. The frequency $v$is doubled?