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Chapter 28: Problem 6

When a particular inductor and capacitor are connected across the same AC voltage, the current in the inductor is higher than in the capacitor. Is this true at all frequencies?

Short Answer

Expert verified
No, the statement is not true for all frequencies. The current in the inductor is higher than in the capacitor only at low frequencies. At high frequencies, the current in the capacitor is higher than in the inductor.

Step by step solution

01

Understand the fundamental relationship

In an AC circuit, the reactance (X) provided by the inductor and the capacitor depends on the frequency (f). The inductive reactance \(X_L = 2\pi fL\) where \(L\) is the inductance. The capacitive reactance is given by \(X_C = 1/(2\pi fC)\) where \(C\) is the capacitance. Since \(X_L\) is directly proportional to \(f\) and \(X_C\) is inversely proportional to \(f\), they change oppositely with a change in the frequency. Hence, the current \(I = V/X\) (where \(V\) is the voltage) in the inductor and the capacitor changes differently with different frequencies.
02

Discuss the effect of frequency on current

At low frequencies, \(X_C\) is high and \(X_L\) is low. Therefore, the current in the capacitor is low and in the inductor is high. Conversely, at high frequencies, \(X_C\) is low and \(X_L\) is high, so the current in the capacitor is high and the inductor is low.
03

Conclusion

From the above discussion, we conclude that the statement 'the current in the inductor is always higher than in the capacitor' is not correct for all frequencies. It is true only at low frequencies.

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Most popular questions from this chapter

A damped \(L C\) circuit consists of a 0.15 -uF capacitor and a \(20-\mathrm{mH}\) inductor with resistance \(1.6 \Omega .\) How many oscillation cycles will occur before the peak capacitor voltage drops to half its initial value?

A step-up transformer increases voltage, or energy per unit charge. Why doesn't this violate energy conservation?

A damped RLC circuit includes a \(5.0-\Omega\) resistor and a \(100-\mathrm{mH}\) inductor. If half the initial energy is lost after 15 cycles, what's the capacitance?

There's an insulating gap between capacitor plates, so how can current flow in an AC circuit containing a capacitor?

If you measure the rms voltages across the resistor, capacitor, and inductor in a series \(R L C\) circuit, will they add to the rms generator voltage?
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