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} $
