UPSC Exam > UPSC Questions > The equation of current in a purely inductive...
Start Learning for Free
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.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup