(II) A capacitor is placed in parallel with some device, B...

(II) A capacitor is placed in parallel with some device, B as in Fig. $18 b ,$ to filter out stray high frequency signals, but to allow ordinary $60 - H z$ ac to pass through with little loss. Suppose that circuit $B$ in Fig. 18$b$ is a resistance $R = 490 \Omega$ connected to ground, and that $C = 0.35 \mu \mathrm { F }$ . What percent of the incoming current will pass through $C$ rather than $R$ if it is $( a )$ it is 60$\mathrm { Hz }$ ; (b) $60,000 \mathrm { Hz }$ ?

Key Concepts

Frequency Filtering

Frequency filtering is the process of selectively allowing signals of certain frequencies to pass while attenuating others. By exploiting the frequency-dependent behavior of components like capacitors, circuits can be designed to target and reduce unwanted high-frequency noise while permitting the desired low-frequency signals to go through, thereby improving signal integrity and performance.

Capacitive Reactance

Capacitive reactance is the opposition a capacitor presents to AC current, quantified by the formula X_C = 1/(2?fC), where f is the frequency and C is the capacitance. This concept is crucial because it shows that a capacitor’s resistance to current decreases as the frequency increases, making it a key component for filtering high-frequency signals while allowing lower frequencies to pass with minimal impedance.

Impedance in AC Circuits

Impedance extends the idea of resistance to AC circuits by incorporating both resistive and reactive (capacitive or inductive) components, and is expressed as a complex quantity. This concept is essential for analyzing and designing AC circuits, as it governs how voltage and current interact within different circuit elements, especially when they are combined in parallel or series configurations.

Current Division in Parallel Circuits

In a parallel circuit, the total current splits between the branches inversely proportional to their impedances. This principle of current division is important in understanding how alternating current divides between a resistor and a capacitor: the branch with lower impedance will carry more current, and changes in frequency will alter the impedance of the capacitor, thus shifting the current division significantly.

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