# ch23 - CHAPTER 23 ALTERNATING CURRENT CIRCUITS ANSWERS TO...

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CHAPTER 23 ALTERNATING CURRENT CIRCUITS ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. (d) According to 2 rms / P V R = (Equation 20.15c), the average power is proportional to the square of the rms voltage. Tripling the voltage causes the power to increase by a factor of 3 2 = 9. 2. I rms = 1.9 A 3. (b) The current I rms through a capacitor depends inversely on the capacitive reactance X C , as expressed by the relation I rms = V rms / X C (Equation 23.1). The capacitive reactance becomes infinitely large as the frequency goes to zero (see Equation 23.2), so the current goes to zero. 4. (e) According to ( 29 C 1/ 2 X f C π = (Equation 23.2) and L 2 X f L π = (Equation 23.4), doubling the frequency f causes X C to decrease by a factor of 2 and X L to increase by a factor of 2. 5. I rms = 1.3 A 6. (a) The component of the phasor along the vertical axis is V 0 sin 2 π f t (see the drawing that accompanies this problem), which is the instantaneous value of the voltage. 7. (b) The instantaneous value of the voltage is the component of the phasor that lies along the vertical axis (see Sections 23.1 and 23.2). This vertical component is greatest in B and least in A, so the ranking is (largest to smallest) B, C, A. 8. (d) In a resistor the voltage and current are in phase. This means that the two phasors are colinear. 9. (c) Power is dissipated by the resistor, as discussed in Section 20.5. On the other hand, the average power dissipated by a capacitor is zero (see Section 23.1). 10. I rms = 2.00 A

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217 ALTERNATING CURRENT CIRCUITS 11. (a) When the rms voltage across the inductor is greater than that across the capacitor, the voltage across the RCL combination leads the current (see Section 23.3). 12. (d) Since I rms = V rms / Z (Equation 23.6), the current is a maximum when the impedance Z is a minimum. The impedance is ( 29 2 2 L C Z R X X = + - (Equation 23.7), and it has a minimum value when X C = X L = 50 . 13. (c) The inductor has a very small reactance at low frequencies and behaves as if it were replaced by a wire with no resistance. Therefore, the circuit behaves as two resistors, R 1 and R 2 , connected in parallel. The inductor has a very large reactance at high frequencies and behaves as if it were cut out of the circuit, leaving a gap in the connecting wires. The circuit behaves as a single resistance R 2 connected across the generator. The situation at low frequency gives rise to the largest possible current, because the effective resistance of the parallel combination is smaller than the resistance R 2 . 14. (a) The capacitor has a very small reactance at high frequencies and behaves as if it were replaced by a wire with no resistance. Therefore, the circuit behaves as two resistors, R 1 and R 2 , connected in parallel. The capacitor has a very large reactance at low frequencies and behaves as if it were cut out of the circuit, leaving a gap in the connecting wires. Therefore, the circuit behaves as a single resistor R 1 connected across the generator. The situation at high frequencies gives rise to the largest possible current, because the effective resistance of the parallel combination is smaller than the resistance R 1 .
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