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The equation of current in a purely inductive
circuit is 5sin(49 it- 30°). If the inductance is
30 mH then the equation for the voltage across
the inductor, will be?
circuit is 5sin(49 it- 30°). If the inductance is
30 mH then the equation for the voltage across
the inductor, will be?
Most Upvoted Answer
The equation of current in a purely inductivecircuit is 5sin(49 it- 30...
To derive the voltage across an inductor in a purely inductive circuit, we can use the relationship between current and voltage in inductors.
Understanding the Current Equation
The given current equation is:
5sin(49 it - 30°)
- Amplitude of current (I) = 5 A
- Angular frequency (ω) = 49 rad/s
- Phase angle (φ) = -30°
Inductor Voltage Relationship
The voltage (V) across an inductor can be calculated using the formula:
V(t) = L * (di/dt)
Where:
- L = inductance (in henries)
- di/dt = derivative of current with respect to time
Calculating di/dt
1. Differentiating the current equation:
- I(t) = 5sin(49t - 30°)
- di/dt = 5 * 49 * cos(49t - 30°)
2. This simplifies to:
- di/dt = 245cos(49t - 30°)
Inductance Value
Given:
- L = 30 mH = 0.03 H
Calculating Voltage
Now substituting values into the voltage formula:
V(t) = L * (di/dt)
- V(t) = 0.03 * 245cos(49t - 30°)
- V(t) = 7.35cos(49t - 30°)
Final Voltage Equation
Therefore, the equation for the voltage across the inductor is:
V(t) = 7.35cos(49t - 30°)
This voltage leads the current by 90°, consistent with the phase relationship in purely inductive circuits.
Understanding the Current Equation
The given current equation is:
5sin(49 it - 30°)
- Amplitude of current (I) = 5 A
- Angular frequency (ω) = 49 rad/s
- Phase angle (φ) = -30°
Inductor Voltage Relationship
The voltage (V) across an inductor can be calculated using the formula:
V(t) = L * (di/dt)
Where:
- L = inductance (in henries)
- di/dt = derivative of current with respect to time
Calculating di/dt
1. Differentiating the current equation:
- I(t) = 5sin(49t - 30°)
- di/dt = 5 * 49 * cos(49t - 30°)
2. This simplifies to:
- di/dt = 245cos(49t - 30°)
Inductance Value
Given:
- L = 30 mH = 0.03 H
Calculating Voltage
Now substituting values into the voltage formula:
V(t) = L * (di/dt)
- V(t) = 0.03 * 245cos(49t - 30°)
- V(t) = 7.35cos(49t - 30°)
Final Voltage Equation
Therefore, the equation for the voltage across the inductor is:
V(t) = 7.35cos(49t - 30°)
This voltage leads the current by 90°, consistent with the phase relationship in purely inductive circuits.
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The equation of current in a purely inductivecircuit is 5sin(49 it- 30°). If the inductance is30 mH then the equation for the voltage acrossthe inductor, will be?
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The equation of current in a purely inductivecircuit is 5sin(49 it- 30°). If the inductance is30 mH then the equation for the voltage acrossthe inductor, will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The equation of current in a purely inductivecircuit is 5sin(49 it- 30°). If the inductance is30 mH then the equation for the voltage acrossthe inductor, will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of current in a purely inductivecircuit is 5sin(49 it- 30°). If the inductance is30 mH then the equation for the voltage acrossthe inductor, will be?.
The equation of current in a purely inductivecircuit is 5sin(49 it- 30°). If the inductance is30 mH then the equation for the voltage acrossthe inductor, will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The equation of current in a purely inductivecircuit is 5sin(49 it- 30°). If the inductance is30 mH then the equation for the voltage acrossthe inductor, will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of current in a purely inductivecircuit is 5sin(49 it- 30°). If the inductance is30 mH then the equation for the voltage acrossthe inductor, will be?.
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