Answer

Verified

382.2k+ views

**Hint:**The magnitude of emf is the rate of change of magnetic flux with respect to time, it reaches its maximum value when the flux curve has the greatest slope.Mutual induction is a phenomenon by which an induced emf is produced in one coil due to change in strength of current flowing through another coil.

**Complete step by step answer:**

Mutual induction is the property of two coils by virtue of which each opposes any change in the strength of current flowing through the other by developing an induced emf. Faraday’s law of Induction states that the induced emf in a circuit is proportional to the time rate of change of magnetic flux through the circuit. i.e,

\[\mathbf{\varepsilon }=\dfrac{-d\varphi }{dt}\]

The negative sign signifies that the induced emf always opposes any change in magnetic flux associated with the circuit.

Now, \[\varphi =Mi\]

where $M$ is the coefficient of mutual induction and $i$ is the current flowing in the coil.

Also,

\[i={{i}_{m}}\sin \mathbf{\omega }t\],

where $\omega$ = the angular velocity and ${i_m}$ = amplitude of electric current.

Now, if we differentiate magnetic flux with respect to time, we get,

\[\varepsilon =\dfrac{-d\varphi }{dt} \\

\Rightarrow \varepsilon =-\dfrac{Md({{i}_{m}}\sin \omega t)}{dt} \\

\Rightarrow \varepsilon=-M{{i}_{m}}\omega \cos \omega t\]

Since, in the above formula only the value of \[\cos \omega t\] varies with time, and it’s value can vary from -1 to +1, for \[\varepsilon ={{\varepsilon }_{\max .}}\], we need to have the value of \[\cos \omega t\] to be -1. So that the overall value becomes positive.So,\[{{\varepsilon }_{\max .}}=M{{i}_{m}}\omega \] and from the question, we get \[M=5 \times {{10}^{-3}}H\], \[{{i}_{m}}=10A\], \[\omega =100\pi rad/s\].Thus

\[{{\mathbf{\varepsilon }}_{\max .}}=0.005 \times 10 \times 100\pi \]

\[\therefore {{\mathbf{\varepsilon }}_{\max .}}=5\pi \]

**Hence, the maximum value of the emf induced in the second coil is $5\pi$.**

**Note:**In order to get the highest value of a quantity that depends on a trigonometric function, look at the formula and try to use one of the known values of that trigonometric function. While using a graph, the maximum value of induced emf is obtained when the flux curve (in ‘magnetic flux vs emf’ graph) has the greatest slope.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

A rainbow has circular shape because A The earth is class 11 physics CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell