
The average and RMS value of voltage for square waves shown in the fig. having a peak value are:

(A)
(B)
(C)
(D) Zero,
Answer
153.3k+ views
Hint: In this solution, we will use the formula of average and RMS value. We only need to consider one cycle of the voltage to calculate the average and RMS value.
Complete step by step answer:
In the graph given to us, we want to calculate the average and RMS value of voltage.
The average amplitude is the mathematical “mean” of all a waveform’s points over the period of one cycle. It can be mathematically calculated as:
We can see that the waveform of the voltage starts a cycle at and ends the cycle at . To calculate the integral of the wave function given to us, we need to break the integral down into regions where the voltage has constant values. So, we can write
The term can be taken out of the integral since it is constant. The integral can then be simplified to
Hence the average voltage will be zero.
Now, The RMS value stands for Root Mean Square value. It is a way of expressing an AC quantity of voltage or current in terms functionally equivalent to DC. It can be mathematically calculated as
The integral can be broken into two parts as
The integral can be simplified as
Or,
Hence the correct choice is option (D).
Note: While calculating the average and the RMS value, we must not forget the term outside the integral. We can also find the average value graphically as zero since the area of the graph for one time period is the same in the positive and negative regime and as such, the average value will be zero.
Complete step by step answer:
In the graph given to us, we want to calculate the average and RMS value of voltage.
The average amplitude is the mathematical “mean” of all a waveform’s points over the period of one cycle. It can be mathematically calculated as:
We can see that the waveform of the voltage starts a cycle at
The
Hence the average voltage will be zero.
Now, The RMS value stands for Root Mean Square value. It is a way of expressing an AC quantity of voltage or current in terms functionally equivalent to DC. It can be mathematically calculated as
The integral can be broken into two parts as
The integral can be simplified as
Or,
Hence the correct choice is option (D).
Note: While calculating the average and the RMS value, we must not forget the
Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
School Full course for MAHARASHTRABOARD students
₹33,300 per year
Recently Updated Pages
JEE Main 2022 (June 29th Shift 2) Maths Question Paper with Answer Key

JEE Main 2023 (January 25th Shift 1) Maths Question Paper with Answer Key

JEE Main 2022 (July 29th Shift 1) Maths Question Paper with Answer Key

JEE Main 2022 (July 26th Shift 2) Chemistry Question Paper with Answer Key

JEE Main 2022 (June 26th Shift 2) Maths Question Paper with Answer Key

JEE Main 2022 (June 29th Shift 1) Physics Question Paper with Answer Key

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Degree of Dissociation and Its Formula With Solved Example for JEE

Displacement-Time Graph and Velocity-Time Graph for JEE

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electrical Field of Charged Spherical Shell - JEE

Ideal and Non-Ideal Solutions Raoult's Law - JEE
