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Chapter 30: Problem 46

What is the maximum value of the AC voltage whose root-mean-square value is (a) \(110 \mathrm{~V}\) or (b) \(220 \mathrm{~V} ?\)

Short Answer

Expert verified
Answer: (a) The maximum value of the AC voltage with an RMS value of 110 V is approximately 155.56 V. (b) The maximum value of the AC voltage with an RMS value of 220 V is approximately 311.13 V.

Step by step solution

01

Write down the given RMS values

We are given the RMS values of two AC voltages as: (a) \(V_\mathrm{rms} = 110 \mathrm{~V}\) (b) \(V_\mathrm{rms} = 220 \mathrm{~V}\)
02

Calculate the maximum value of the AC voltage for part (a)

Using the relationship between the maximum value and the RMS value of an AC voltage, we can find the maximum value for part (a): \(V_\mathrm{max} = \sqrt{2} \times V_\mathrm{rms}\) For part (a), \(V_\mathrm{rms} = 110 \mathrm{~V}\), so we have: \(V_\mathrm{max} = \sqrt{2} \times 110 \mathrm{~V} \approx 155.56 \mathrm{~V}\)
03

Calculate the maximum value of the AC voltage for part (b)

Similarly, we can find the maximum value for part (b). For part (b), \(V_\mathrm{rms} = 220 \mathrm{~V}\), so we have: \(V_\mathrm{max} = \sqrt{2} \times 220 \mathrm{~V} \approx 311.13 \mathrm{~V}\)
04

Write down the final answers

The student can now write the final answers for the maximum value of the AC voltage for both given RMS values: (a) The maximum value of the AC voltage with an RMS value of \(110 \mathrm{~V}\) is approximately \(155.56 \mathrm{~V}\). (b) The maximum value of the AC voltage with an RMS value of \(220 \mathrm{~V}\) is approximately \(311.13 \mathrm{~V}\).

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Most popular questions from this chapter

Laboratory experiments with series RLC circuits require some care, as these circuits can produce large voltages at resonance. Suppose you have a 1.00 - \(\mathrm{H}\) inductor (not difficult to obtain) and a variety of resistors and capacitors. Design a series RLC circuit that will resonate at a frequency (not an angular frequency) of \(60.0 \mathrm{~Hz}\) and will produce at resonance a magnification of the voltage across the capacitor or the inductor by a factor of 20.0 times the input voltage or the voltage across the resistor.

The quality factor, \(Q\), of a circuit can be defined by \(Q=\omega_{0}\left(U_{E}+U_{B}\right) / P .\) Express the quality factor of a series RLC circuit in terms of its resistance \(R\), inductance \(L\), and capacitance \(C .\)

A circuit contains a \(100 .-\Omega\) resistor, a \(0.0500-\mathrm{H}\) inductor, a \(0.400-\mu \mathrm{F}\) capacitor, and a source of time-varying emf connected in series. The time-varying emf corresponds to \(V_{\mathrm{rms}}=50.0 \mathrm{~V}\) at a frequency of \(2000 . \mathrm{Hz}\). a) Determine the current in the circuit. b) Determine the voltage drop across each component of the circuit. c) How much power is drawn from the source of emf?

A 2.00 - \(\mu\) F capacitor was fully charged by being connected to a 12.0 - \(V\) battery. The fully charged capacitor is then connected in series with a resistor and an inductor: \(R=50.0 \Omega\) and \(L=0.200 \mathrm{H}\). Calculate the damped frequency of the resulting circuit.

An inductor with inductance \(L=47.0 \mathrm{mH}\) is connected to an AC power source having a peak value of \(12.0 \mathrm{~V}\) and \(f=1000 . \mathrm{Hz} .\) Find the reactance of the inductor and the maximum current in the circuit.
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