Problem 31.63 In an L-R-C series circuit, the source has a voltage amplitude of

Question

Problem 31.63

In an L-R-C series circuit, the source has a voltage amplitude of 123V , R = 78.0? , and the reactance of the capacitor is 479? . The voltage amplitude across the capacitor is 366V .

Part A

What is the current amplitude in the circuit?

I=........... A

Part B

What is the impedance?

Z=........... Omega

Part C

What two values can the reactance of the inductor have?

Enter your answers in ascending order separated by a comma.

X_L=............. omega

Part D

For which of the two values found in part (c) is the angular frequency less than the resonance angular frequency?

A)he less value of XL

B)the larger value of XL

Explanation / Answer

(a)

   from the ohms law we can write

   VC = I XC

   the current amplitude in the circuit will be    

I = VC / XC

    = 366 V / 479 ?

    = 0.764 amps

(b)

   the impedence Z will be

   Z = V / I

      = 123 V / 0.764

      = 160.98 ?

(c)

   the expression for the impedence is givenby

   Z = ?[R2 + (XL -XC)2]

   we get the inductive reactance as

   XL = XC

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