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What is the impedance of a capacitor in an AC circuit at frequency f?
What is the impedance of a capacitor in an AC circuit at frequency f?
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Practice Questions
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Q1
What is the impedance of a capacitor in an AC circuit at frequency f?
Z_C = 1 / (jωC)
Z_C = jωC
Z_C = R + jX_C
Z_C = R - jX_C
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The impedance of a capacitor in an AC circuit is given by Z_C = 1 / (jωC), where ω = 2πf is the angular frequency.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the impedance of a capacitor in an AC circuit at frequency f?
Solution:
The impedance of a capacitor in an AC circuit is given by Z_C = 1 / (jωC), where ω = 2πf is the angular frequency.
Steps: 7
Show Steps
Step 1: Understand that impedance (Z) is a measure of how much a circuit resists the flow of alternating current (AC).
Step 2: Know that a capacitor is a component that stores electrical energy in an electric field.
Step 3: Recognize that in an AC circuit, the impedance of a capacitor depends on the frequency of the AC signal.
Step 4: Learn the formula for the impedance of a capacitor: Z_C = 1 / (jωC).
Step 5: Identify that 'j' is the imaginary unit, 'ω' (omega) is the angular frequency, and 'C' is the capacitance of the capacitor.
Step 6: Calculate the angular frequency using the formula: ω = 2πf, where 'f' is the frequency of the AC signal.
Step 7: Substitute ω into the impedance formula to find the impedance of the capacitor at frequency f.
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