Question

The instantaneous value of emf is, \[E = 140\sin 300t\] . What is the peak value of voltage and rms voltage?

Answer 1

Hint:Initially, we start by analysing the data given to us. We then remember the formula for instantaneous voltage. We compare the given formula to the standard formula and arrive at a value for root mean square voltage and peak voltage,

Formulas used:
The formula of finding instantaneous emf is given as,
\[E = {E_0}\sin \omega t\]
Where \[{E_0}\] is the peak voltage of the system, \[\omega \] is the angular frequency of the system and \[t\] is the time.
The formula to find the rms voltage is given by,
\[{E_{rms}} = \dfrac{{{E_0}}}{{\sqrt 2 }}\]

Complete step by step answer:
Let us start by remembering the standard equation to find the value of instantaneous emf, \[E = {E_0}\sin \omega t\]
Now let us see the value of instantaneous voltage given to us, \[E = 140\sin 300t\].
We then compare the values and analyse the values and find what the peak voltage is.
The peak voltage value by comparing with the standard equation is, \[{E_0} = 140V\].
We apply this value on the equation to find the value of the rms voltage,
\[{E_{rms}} = \dfrac{{{E_0}}}{{\sqrt 2 }}\]
We apply the found values to this equation and get the value for rms voltage as,
\[{E_{rms}} = \dfrac{{{E_0}}}{{\sqrt 2 }} \\
\Rightarrow {E_{rms}} = \dfrac{{140}}{{\sqrt 2 }} \\
\therefore {E_{rms}} = 98.99V\]

In conclusion the peak voltage of the system is \[140V\] and the rms voltage of the system is \[98.99V\].

Note:EMF or electromotive force is the energy per unit electric charge that is imprinted by an energy source. Instantaneous emf is that emf value at a particular instant of time. The peak value of emf is that value of emf where the flux curve has maximum slope. When the slope is zero induced emf also goes to zero.