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AC Through an Inductor and Capacitor
An ideal inductor and capacitor oppose alternating current through frequency-dependent reactance and create phase differences between voltage and current.
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AC Through an Inductor and Capacitor
An inductor makes current fall behind voltage.
A capacitor makes current get ahead of voltage.
Their opposition to AC depends on frequency.
Recommended for Class 12
AC Through an Inductor and Capacitor
Definition
An ideal inductor and capacitor oppose alternating current through frequency-dependent reactance and create phase differences between voltage and current.
Pure Inductor
Inductive reactance:
**XL=ωL=2πfL**
RMS current:
**I=VXL**
In a pure inductor:
current lags voltage by 90°.
Increasing frequency increases `X_L`.
Pure Capacitor
Capacitive reactance:
**XC=1ωC=12πfC**
RMS current:
**I=VXC**
In a pure capacitor:
current leads voltage by 90°.
Increasing frequency decreases `X_C`.
Memory Rule
L → current Lags
C → current Comes first
Formula / Key Relation
**XL=ωL**
**XC=1ωC**
Inductor:
I lags V by 90°
Capacitor:
I leads V by 90°
AC Through an Inductor and Capacitor — Advanced
Ideal inductive and capacitive impedances are imaginary quantities with opposite signs, producing ±90° phase relationships and zero average real power over a complete cycle.
Common Mistakes
Common Mistakes
- Mistake
Do not interchange `X_L` and `X_C`.
- Mistake
Do not say both reactances increase with frequency.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Inductive reactance rises with frequency; capacitive reactance falls with frequency.
A pure inductor has reactance `XL=2πfL`, which increases with frequency, and its current lags voltage by 90°. A pure capacitor has reactance `XC=12πfC`, which decreases as frequency rises, and its current leads voltage by 90°. Both reactances are measured in ohms.
- Definition
- A pure inductor has reactance `XL=2πfL`, which increases with frequency, and its current lags voltage by 90°. A pure capacitor has reactance `XC=12πfC`, which decreases as frequency rises, and its current leads voltage by 90°. Both reactances are measured in ohms.
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Practice
PQ
Q1. Write XL formula
PQ
Q2. Write XC formula
PQ
Q3. Phase in inductor?
PQ
Q4. Phase in capacitor?
PQ
Q5. What happens to XL if frequency doubles?
Exam Practice
EQ
Q1. Explain AC through an ideal inductor
EQ
Q2. Define inductive reactance
EQ
Q3. Explain AC through an ideal capacitor
EQ
Q4. Define capacitive reactance
EQ
Q5. Compare XL and XC with frequency
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.