Electro Magnetic Induction And Alternating Currents Question 472

Question: An equilateral triangular loop having a resistance R and length of each side $ \ell $ is placed in magnetic field which is varying at $ \frac{dB}{dt}=1,T/s $ . The induced current in the loop will be

Options:

A) $ \frac{\sqrt{3}}{4}\frac{{{\ell }^{2}}}{R} $

B) $ \frac{4}{\sqrt{3}}\frac{{{\ell }^{2}}}{R} $

C) $ \frac{\sqrt{3}}{4},\frac{R}{{{\ell }^{2}}} $

D) $ \frac{4}{\sqrt{3}}\frac{R}{{{\ell }^{2}}} $

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \phi =\frac{\sqrt{3}}{4}{{\ell }^{2}}B $ $ \varepsilon =| . \frac{d\phi }{dt} | .=\frac{\sqrt{3}}{4}{{\ell }^{2}}\frac{dB}{dt} $ $ i=\frac{\varepsilon }{R}=\frac{\sqrt{3}{{\ell }^{2}}}{4R} $


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