A capacitor used to provide steady voltages in the power...

A capacitor used to provide steady voltages in the power supply of a stereo amplifier charges rapidly to $35 \mathrm{V}$ every $1 / 60$ second. It must then hold that voltage to within $1.0 \mathrm{V}$ for the next $1 / 60 \mathrm{s}$ while it discharges through the amplifier. If the amplifier draws 1.2 A from the $35-\mathrm{V}$ supply, (a) what's its effective resistance, and (b) what capacitance is needed?

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Key Concepts

Effective Resistance

Effective resistance in the context of power supply circuits represents the load's opposition to current flow, computed from the relationship between the voltage drop and the current drawn (R = ?V/I). This concept simplifies a complex load behavior into a single resistive element for analysis, such as determining how much voltage loss occurs when current flows through the amplifier.

Capacitance and Discharge Behavior

Capacitance is the measure of a capacitor's ability to store electrical charge, and it directly influences how much a capacitor can maintain a voltage under load. The discharge behavior is characterized by the relation ?V = I·?t/C, which shows that for a given current draw over a specific time period, the capacitance must be large enough to limit the voltage drop to a desired level.

RC Circuit Time Constant

The RC time constant (? = R·C) defines the rate at which voltage decays in a resistor-capacitor (RC) circuit. This concept is crucial when analyzing transient responses, as it helps determine how quickly a capacitor discharges through a resistive load and thus ensures that the voltage remains steady over the necessary time interval to power the amplifier.

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