Question

A 130? resistor, a 0.100?F capacitor, and a 290mH inductor are connected in series to a voltage source with amplitude 240V .

A)What is the maximum voltage across the inductor at resonance?

B)What is the maximum energy stored in the capacitor at resonance?

C)What is the maximum energy stored in the inductor at resonance?

Answer 1

at resonance condition

W=sqrt(1/LC)

=sqrt(1/290*10^-3*0.1*10^-6)

=sqrt(0.034*10⁹)

=sqrt(0.34*10⁸)

=0.583*10⁴

2*3.14*f=0.583*10⁴

f=928.4HZ

X_L=WL

=0.583*10⁴*290*10^-3

=1690.7ohms

V=IX_L ASSUME RESISTOR IN KILO OHMS I DO NOT KNOW WHAT IS MEAN BY QUESTION MARK

I=240/130*10³

=1.846*10^-3A

A)

V=1.846*10^-3*1690.7

=3.121volts

C)

energy stored in the inductor at resonance

=0.5LI²

=0.5*290*10^-3*1.846²*10^-6

=0.494*10^-6J

B)

maximum energy stored in the capacitor at resonance

=0.5*CV²

voltage across capacitor

X_C=1/WC

=1/0.583*10⁴*0.1*10^-6

=17.152*10^-2ohms

V=IX_C

=1.846*10^-3*17.152*10^-2

=31.66*10^-5volts

E=0.5*0.1*10^-6*31.66²*10^-10

=50.11*10^-16J