Answer
Verified
444.9k+ views
Hint: To solve the above given problem we should know how we can calculate the induced emf in any coil, if the flux is given. Principle of transformer is based on the principle of mutual induction and as we all know that the Faraday's law states that the Induced EMF is equal to the rate of change of magnetic flux.
Complete answer:
So, from the faraday’s law, we get
Since the rate of change of magnetic flux is the induced emf,
So, Induced emf= \[e = \dfrac{{d\phi }}{{dt}}\], where $e = $induced emf, $\phi = $flux associated with the coil.
So, for the transformer we can get the induced emf in the primary coil from the given magnetic flux linked with the primary coil, that is \[\phi = {\phi _0} + 4t,\;\]
So, the induced emf in the primary coil= ${e_p} = \dfrac{{d\phi }}{{dt}} = \dfrac{d}{{dt}}({\phi _0} + 4t)$
$ \Rightarrow {e_p} = (0 + 4)$
$ \Rightarrow {e_p} = 4V$--------equation (1)
Hence the induced voltage in the primary coil is ${e_p} = 4V$.
In the question number of the turns in the primary coil and the secondary coil is given, So from this we can get the transformation ratio, $k$
So, transformation ratio, $k = \dfrac{{{N_s}}}{{{N_p}}}$
$ \Rightarrow k = \dfrac{{{N_s}}}{{{N_p}}} = \dfrac{{1500}}{{50}}$ (putting the values ${N_s} = 1500$ and ${N_p} = 50$)
$ \Rightarrow k = 30$-----equation (2)
Also, the relation between the transformation ratio and the induced emfs in the primary and secondary is as follows,
$ \Rightarrow k = \dfrac{{{e_s}}}{{{e_p}}}$
Putting the value of the ${e_s}$ from equation (1), we get
$ \Rightarrow k = \dfrac{{{e_s}}}{4}$-----equation (3)
Now from equation (2) and equation (3), we get
$ \Rightarrow 30 = \dfrac{{{e_s}}}{4}$
$ \Rightarrow {e_p} = 120V$
So, the correct answer is “Option C”.
Note:
Since Induced EMF is equal to the rate of change of magnetic flux, and the magnetic flux is equal to Magnetic field strength multiplied by the Area =$BA$.
Therefore,\[Induced{\text{ }}EMF\; = \dfrac{{\left( {change{\text{ }}in{\text{ }}Magnetic{\text{ }}Flux{\text{ }}Density{\text{ }}x{\text{ }}Area} \right)}}{{change{\text{ }}in{\text{ }}Time}}\]
Therefore, \[Induced{\text{ }}EMF\; = \dfrac{{(B\pi {r^2}n)}}{t}\]
Complete answer:
So, from the faraday’s law, we get
Since the rate of change of magnetic flux is the induced emf,
So, Induced emf= \[e = \dfrac{{d\phi }}{{dt}}\], where $e = $induced emf, $\phi = $flux associated with the coil.
So, for the transformer we can get the induced emf in the primary coil from the given magnetic flux linked with the primary coil, that is \[\phi = {\phi _0} + 4t,\;\]
So, the induced emf in the primary coil= ${e_p} = \dfrac{{d\phi }}{{dt}} = \dfrac{d}{{dt}}({\phi _0} + 4t)$
$ \Rightarrow {e_p} = (0 + 4)$
$ \Rightarrow {e_p} = 4V$--------equation (1)
Hence the induced voltage in the primary coil is ${e_p} = 4V$.
In the question number of the turns in the primary coil and the secondary coil is given, So from this we can get the transformation ratio, $k$
So, transformation ratio, $k = \dfrac{{{N_s}}}{{{N_p}}}$
$ \Rightarrow k = \dfrac{{{N_s}}}{{{N_p}}} = \dfrac{{1500}}{{50}}$ (putting the values ${N_s} = 1500$ and ${N_p} = 50$)
$ \Rightarrow k = 30$-----equation (2)
Also, the relation between the transformation ratio and the induced emfs in the primary and secondary is as follows,
$ \Rightarrow k = \dfrac{{{e_s}}}{{{e_p}}}$
Putting the value of the ${e_s}$ from equation (1), we get
$ \Rightarrow k = \dfrac{{{e_s}}}{4}$-----equation (3)
Now from equation (2) and equation (3), we get
$ \Rightarrow 30 = \dfrac{{{e_s}}}{4}$
$ \Rightarrow {e_p} = 120V$
So, the correct answer is “Option C”.
Note:
Since Induced EMF is equal to the rate of change of magnetic flux, and the magnetic flux is equal to Magnetic field strength multiplied by the Area =$BA$.
Therefore,\[Induced{\text{ }}EMF\; = \dfrac{{\left( {change{\text{ }}in{\text{ }}Magnetic{\text{ }}Flux{\text{ }}Density{\text{ }}x{\text{ }}Area} \right)}}{{change{\text{ }}in{\text{ }}Time}}\]
Therefore, \[Induced{\text{ }}EMF\; = \dfrac{{(B\pi {r^2}n)}}{t}\]
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
Which are the Top 10 Largest Countries of the World?
Who was the Governor general of India at the time of class 11 social science CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Difference Between Plant Cell and Animal Cell