A capacitor is connected to an ac generator that has a frequency of 3.4 kHz and produces a volta

step 1 So in this problem we're considering a capacitor that is connected to an alternating current gen

A capacitor is connected to an ac generator that has a...

A capacitor is connected to an ac generator that has a frequency of $3.4 \mathrm{kHz}$ and produces a voltage of $2.0 \mathrm{V}$. The current in the capacitor is $35 \mathrm{mA}$. When the same capacitor is connected to a second ac generator that has a frequency of $5.0 \mathrm{kHz},$ the current in the capacitor is $85 \mathrm{mA}$. What voltage does the second generator produce?

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Key Concepts

AC Circuit Voltage-Current Relationship

In AC circuits, the relationship between voltage, current, and impedance (which includes both resistance and reactance) is given by Ohm's law in phasor form, V = IZ. For a capacitor, this relationship becomes V = I Xc. Understanding this relationship is essential for determining how changes in frequency impact the current or voltage in the circuit when one of these quantities is varied.

Frequency Dependence

The behavior of capacitors in AC circuits is strongly frequency-dependent. As the frequency increases, the capacitive reactance decreases, allowing more current to flow for the same voltage. This dependency is critical when comparing the performance of a capacitor under different AC frequencies, and it forms the basis for analyzing circuits such as filters and tuning circuits.

Capacitive Reactance

Capacitive reactance is the opposition that a capacitor offers to AC current, quantified by the formula Xc = 1/(?C), where ? is the angular frequency and C is the capacitance. It shows that a capacitor’s impedance is inversely proportional to both the frequency of the applied voltage and its capacitance, which directly affects how much current flows for a given voltage in an AC circuit.

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