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In an RLC circuit such as that of the figure assume that R = 4.21 Ω, L = 78.5 mH, fd = 49.9 Hz, and εm = 38.0 V. For what values of the capacitance would the average rate at which energy is dissipated in the resistance be (a) a maximum and minimum? What are (b) the maximum dissipation rate and the corresponding phase angle and power factor? What are (c) the minimum dissipation rate and the corresponding phase angle and  power factor?

The image depicts an RLC series circuit, which consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series with an alternating current (AC) source. ### Circuit Components: 1. **AC Voltage Source (\(\mathcal{E}\))**: - Represents an AC power supply that provides sinusoidal voltage. - Indicated by a circle with a sine wave inside and a positive notation on the left side. 2. **Resistor (R)**: - Symbolized by a zigzag line. - Opposes the flow of current, causing a voltage drop proportional to the current. 3. **Inductor (L)**: - Represented by a coiled line. - Stores energy in a magnetic field when current passes through it, opposing changes in current flow. 4. **Capacitor (C)**: - Shown as two parallel lines with a gap in between. - Stores energy in an electric field and blocks DC currents while allowing AC currents to pass. ### Current Indication: - The current (\(i\)) is indicated along the circuit path, showing the flow from the AC source, through R, L, and finally C. - The direction of current flow is marked by arrows along the circuit. This RLC circuit is typically used to study the behavior of circuits in response to AC voltage, including the phase relationships and impedance at various frequencies. Understanding these components is crucial for analyzing circuit performance in electronics and electrical engineering fields.
Transcribed Image Text:The image depicts an RLC series circuit, which consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series with an alternating current (AC) source. ### Circuit Components: 1. **AC Voltage Source (\(\mathcal{E}\))**: - Represents an AC power supply that provides sinusoidal voltage. - Indicated by a circle with a sine wave inside and a positive notation on the left side. 2. **Resistor (R)**: - Symbolized by a zigzag line. - Opposes the flow of current, causing a voltage drop proportional to the current. 3. **Inductor (L)**: - Represented by a coiled line. - Stores energy in a magnetic field when current passes through it, opposing changes in current flow. 4. **Capacitor (C)**: - Shown as two parallel lines with a gap in between. - Stores energy in an electric field and blocks DC currents while allowing AC currents to pass. ### Current Indication: - The current (\(i\)) is indicated along the circuit path, showing the flow from the AC source, through R, L, and finally C. - The direction of current flow is marked by arrows along the circuit. This RLC circuit is typically used to study the behavior of circuits in response to AC voltage, including the phase relationships and impedance at various frequencies. Understanding these components is crucial for analyzing circuit performance in electronics and electrical engineering fields.
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