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 = 2.30 H) are connected in series across a 2.40 102-Hz AC source for which

Vmax = 1.30 102 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

a) f = 240 Hz

XL = 2 pi f L = 2 x pi x 240 x 2.30 = 3468.32 ohm

Xc = 1 / 2pifC = 1 / (2 x pi x 240 x 0.250 x 10^-6) = 2652.58 ohm

R = 900 ohm

Z = R + j(XL - Xc)

|Z| = sqrt[ R^2 + (xL - Xc)^2 ] = 1214.67 ohm

b) Imax = Vmax / Z = 120 / 1214.67 = 0.107 A

c) phase angle = tan^-1 [ (XL - Xc) / R ] = 42.20 deg

d) The current lags behind the voltage

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