Question
Download Solution PDFSine Wave Peak to peak = ____
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The RMS value of a sinusoidal wave is given by:
\(V_{rms}=\frac{V_m}{√2}\)
Where Vm is the peak voltage of the sine wave.
Derivation:
A general sinusoidal wave can be expressed as:
v(t) = Vm sin (ωt)
Vm = Peak Value
ω = Angular frequency
RMS value 'or' the effective value of an alternating quantity is calculated as:
\({V_{rms}} = √{\frac{1}{T}\mathop \smallint \limits_0^T {v^2}\left( t \right)dt} \)
T = Time period
\({V_{rms}} = √{\frac{1}{T}\mathop \smallint \limits_0^T {V_m^2~sin^2}\left( \omega t \right)dt} \)
\({V_{rms}} = √{\frac{1}{T}\mathop \smallint \limits_0^T \frac{V_m^2-V_m^2~cos(2\omega t)} {2} dt}\)
\({V_{rms}} = √{\frac{1}{T}(\frac{V_m^2} {2}) [t]_0^T}\)
\({V_{rms}} = √{\frac{V_m^2} {2}}\)
\({V_{rms}} = \frac{V_m} {√{{2}}}\)
Peak to peak value = 2Vm
2Vm = Vrms × 2√2
2Vm = Vrms × √8
The average value of sinusoidal waveform over one complete cycle is zero as two halves cancel each other, so the average value is taken over half a cycle.
\({V_{avg}} = \frac{1}{\pi }\mathop \smallint \nolimits_0^\pi {V_p}\sin \theta \;d\theta \)
\({V_{avg}} = \frac{{2{V_p}}}{\pi } = 0.637 × {V_p}\)
Last updated on Jun 11, 2025
-> The RRB NTPC Admit Card 2025 has been released on 1st June 2025 on the official website.
-> The UPSC Prelims Result 2025 and UPSC IFS Result 2025 has been released @upsc.gov.in
-> Railway Recruitment Board activated the RRB ALP application form 2025 correction link, candidates can make the correction in the application form till 31st May 2025.
-> The Railway Recruitment Board (RRB) has released the official RRB ALP Notification 2025 to fill 9,970 Assistant Loco Pilot posts.
-> The Railway Recruitment Board (RRB) has released the official RRB ALP Notification 2025 to fill 9,970 Assistant Loco Pilot posts.
-> The official RRB ALP Recruitment 2025 provides an overview of the vacancy, exam date, selection process, eligibility criteria and many more.
->The candidates must have passed 10th with ITI or Diploma to be eligible for this post.
->The RRB Assistant Loco Pilot selection process comprises CBT I, CBT II, Computer Based Aptitude Test (CBAT), Document Verification, and Medical Examination.
-> This year, lakhs of aspiring candidates will take part in the recruitment process for this opportunity in Indian Railways.
-> Serious aspirants should prepare for the exam with RRB ALP Previous Year Papers.
-> Attempt RRB ALP GK & Reasoning Free Mock Tests and RRB ALP Current Affairs Free Mock Tests here