A resistor ( R = 9.00 10 2 ), a capacitor ( C = 0.250 F), and an inductor ( L =

Question

A resistor

(R = 9.00 102 ),

a capacitor

(C = 0.250 F),

and an inductor

(L = 1.80 H)

are connected in series across a 2.40 102-Hz AC source for which

Vmax = 1.05 102 V.

(a) Calculate the impedance of the circuit.
k

(b) Calculate the maximum current delivered by the source.
A

(c) Calculate the phase angle between the current and voltage.
°

(d) Is the current leading or lagging behind the voltage?

The current leads the voltage.The current lags behind the voltage.    There is no phase difference between the current and voltage

Explanation / Answer

R = 900 , C = 0.25 F, L = 1.8 H

f = 240 Hz, V = 105 V

XL = wL = 2pi*f*L = 2pi*240*1.8 = 2714.34 ohm

Xc = 1/2pi*f*C = 2652.58 ohm

X = XL - Xc = 61.76 ohm

a) Impedence = Z = sqrt[R^2 + X^2] = 902.12 ohm

b) the maximum current = I = V/Z = 0.116 A

c) X = XL – XC = 61.76 ohm (Inductive)

phase angle = sin-1 (61.76/900) = 3.93 degrees.

d) the reactance is Inductive, The current lags behind the voltage.

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