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Difficulty: HardCapacitors

An electronics technician is analyzing an AC circuit that consists of a capacitor connected directly across an alternating current signal generator. If the generator's operating frequency is doubled while the source voltage remains constant, which of the following statements correctly describes the effect on the capacitive reactance and the circuit current?

  1. A
    The capacitive reactance doubles, which causes the circuit current to decrease by half.
  2. The capacitive reactance decreases by half, which causes the circuit current to double.Answer
  3. C
    The capacitive reactance remains constant, which results in no change to the circuit current.
  4. D
    The capacitive reactance drops to zero, because the dielectric begins conducting continuous current at higher frequencies.

Answer

The capacitive reactance decreases by half, which causes the circuit current to double.
Capacitive reactance is calculated using XC=12πfCX_C = \frac{1}{2\pi f C}, which shows that reactance is inversely proportional to the AC frequency. When the frequency is doubled, the opposition to AC current is halved. According to Ohm's law for AC circuits (I=VXCI = \frac{V}{X_C}), reducing the reactance by half while holding the voltage constant doubles the current flowing through the circuit.

Step-by-Step Solution

1
Identify the formula for capacitive reactance
XC=12πfCX_C = \frac{1}{2\pi f C}
Capacitive reactance (XCX_C) measures the opposition a capacitor presents to alternating current and depends inversely on frequency (ff) and capacitance (CC).
2
Determine the change in capacitive reactance when frequency doubles
XC,new=12π(2f)C=12XCX_{C,\text{new}} = \frac{1}{2\pi (2f) C} = \frac{1}{2} X_C
Because frequency is in the denominator, doubling ff halves the total capacitive reactance.
3
Apply Ohm's law for AC circuits to find the change in current
Inew=VXC,new=V12XC=2×(VXC)=2II_{\text{new}} = \frac{V}{X_{C,\text{new}}} = \frac{V}{\frac{1}{2}X_C} = 2 \times \left(\frac{V}{X_C}\right) = 2I
With constant source voltage VV, cutting the opposition to current (XCX_C) by half causes the circuit current to double.

Key Concept

Capacitive Reactance and AC Frequency Relationship
Estimated Time:1m 0s
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Topics

Capacitors

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