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Sinusoidal AC Voltage and Current
A sinusoidal alternating current or voltage changes with time according to a sine or cosine function.
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Sinusoidal AC Voltage and Current
A sine-wave AC rises smoothly from zero to a maximum, returns to zero, becomes negative, reaches a negative maximum and returns to zero.
Then the cycle repeats.
Recommended for Class 12
Sinusoidal AC Voltage and Current
Definition
A sinusoidal alternating current or voltage changes with time according to a sine or cosine function.
Instantaneous Value
An ideal sinusoidal voltage can be represented as:
**v = V₀ sin(ωt)**
Similarly:
**i = I₀ sin(ωt)**
where:
0 = peak voltage
0 = peak current
0 = angular frequency
0 = time.
Angular frequency is:
**ω = 2πf**
Therefore:
**ω = 2π/T**
A complete cycle corresponds to:
**2π radians = 360°**
At any instant `t`, the equation gives the voltage or current existing at that particular moment.
Positive and Negative Half-Cycles
Positive sign represents one chosen direction.
Negative sign represents the opposite direction.
Formula / Key Relation
**v=V₀sin(ωt)**
**i=I₀sin(ωt)**
**ω=2πf**
Sinusoidal AC Voltage and Current — Advanced
A sinusoidal signal is described by amplitude and phase angle:
**θ=ωt**
More generally:
**v=V₀sin(ωt+φ)**
where `φ` represents an initial phase.
Common Mistakes
Common Mistakes
- Mistake
Do not confuse angular frequency `ω` with ordinary frequency `f`.
- Mistake
`ω` is measured in rad/s.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Sinusoidal AC varies smoothly according to a sine function.
Sinusoidal AC can be represented by `v=V₀sin(ωt)` or `i=I₀sin(ωt)`. `V₀` and `I₀` are peak values. Angular frequency is related to ordinary frequency by `ω=2πf`. One complete cycle corresponds to `2π` radians. Positive and negative half-cycles represent opposite directions according to the chosen sign convention.
- Definition
- Sinusoidal AC can be represented by `v=V₀sin(ωt)` or `i=I₀sin(ωt)`. `V₀` and `I₀` are peak values. Angular frequency is related to ordinary frequency by `ω=2πf`. One complete cycle corresponds to `2π` radians. Positive and negative half-cycles represent opposite directions according to the chosen sign convention.
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Practice
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Q1. Write sinusoidal voltage equation
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Q2. Define peak value
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Q3. Write angular-frequency relation
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Q4. Find ω for 50 Hz
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Q5. What does a negative AC value indicate?
Exam Practice
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Q1. Explain sinusoidal AC
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Q2. Define peak and instantaneous values
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Q3. Derive the relation `ω=2πf`
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Q4. Explain positive and negative half-cycles
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Q5. Solve sinusoidal AC problems
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.