Lecture 13

final part

Series RLC in alternating current

The voltage in a capacitor lagsbehind the current by a phase angle of 90 degrees

The current is in phase with the voltage across the resistor

The voltage in an inductor leads the current by a phase angle of90 degrees.

ΔvR =ImaxR sin ωt=ΔVR sin ωt

ΔvL =Imax XL sin ωt+ π2

⎛

⎝⎜⎞

⎠⎟

ΔvC =Imax XC sin ωt−π2

⎛

⎝⎜⎞

⎠⎟

R

XX

V

VV CL

R

CL

tan

phase angle between current and total voltage

I =V0

Zsin ωt( )

V =V0 sin ωt+( )

Series RLC in alternating current

I =V0

Zsin ωt−( )

V =V0 sin ωt( )≡

( )22L CZ R X X≡ + −

RLC NOT in series

Z and φ are NOT as in a series RLC.

Circuit can be solved usingKirchhoff’s rules.

Limiting behavior: when the frequency is very high or very low

very large f,

XC → 0XL → ∞

very small f

XC → ∞XL → 0

Xc= (open gap)XL=0 (shortcut)

∞very LOW frequency

XL= (open gap)Xc= 0 (shortcut)

∞very HIGH frequency

Conceptual Example 4 The Limiting Behavior ofCapacitors and Inductors

The rms voltage of the generator is the same in eachcase. The values of the resistance, capacitance, andinductance are the same. The frequency of the ac generator is very near zero.

In which circuit does the generator supply more rmscurrent?