A 160 resistor, a 0.110 F capacitor, and a 300 mH inductor are connected in seri

Question

A 160 resistor, a 0.110 F capacitor, and a 300 mH inductor are connected in series to a voltage source with amplitude 240 V .

Part A

What is the resonance angular frequency?

Part B

What is the maximum current in the resistor at resonance?

Part C

What is the maximum voltage across the capacitor at resonance?

Part D

What is the maximum voltage across the inductor at resonance?

Part E

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

Part F

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

Explanation / Answer

part A :

Angular Frequency W = 2pif or 1/sqrt(LC)

L is inductance = 0.3 H

C is capaciatnce = 0.11 *10^-6 F

Wo = 1/sqrt(0.3 * 0.11*10^-6)

Wo = 5505 rad/s

----------------------

part B :

max Currrent Imax = V/R

Imax = 240/160

Imax = 1.5 Amps

-------------------

part C:

Vmax = Imax *R = 1.5* 160 = 240 Volts

----------------------
part D:

Vmax across Inductor VL = i* XL

VL = 1.5* wL

VL = 1.5 * 5505 * 0.3

VL = 2477.5 Volts

----------------

part E:

V max across Capacitor

Vc = i Xc

Vc = i/wC

Vc = 1.5/(5505 * 0.11*10^-6)

Vc = 2477.5 Volts

------------

part F :

Max Energy = 0.5 LI^2

Umax = 0.5 * 0.3* 1.5^2

Umax = 0.3375 Joules

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