SATHEE: Electro Magnetic Induction And Alternating Currents Question 167

Electro Magnetic Induction And Alternating Currents Question 167

Question: Determine the rms value of a semi-circular current wave which has a maximum value of a.

Options:

A) $(1 \sqrt{2}) a$

B) $(\sqrt{3 / 2}) a$

C) $(\sqrt{2 / 3}) a$

D) $(\sqrt{1 / 3}) a$

Show Answer

Answer:

Correct Answer: C

Solution:

The equation of a semi - circular wave is

$x^{2} + y^{2} = a^{2}$

or $y^{2} = a^{2} - x^{2}$

$I_{r m s} = \sqrt{\frac{1}{2 a} \int_{- a}^{+ a} y^{2} d x}$

$I_{r m s}^{2} = \frac{1}{2 a} \int_{- a}^{+ a} (a^{2} - x^{2}) d x$

$= \frac{1}{2 a} \int_{- a}^{+ a} (a^{2} - x^{2}) d x = \frac{1}{2 a} | a .^{2} x - \frac{x^{3}}{3} | ._{- a}^{+ a}$

$= \frac{1}{2 a} (a^{3} - \frac{a^{3}}{3} + a^{3} - \frac{a^{3}}{3}) = \frac{2 a^{2}}{3}$

$I_{r m s} = \sqrt{\frac{2 a^{2}}{3}} = \sqrt{\frac{2}{3}} a$

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Electro Magnetic Induction And Alternating Currents Question 167

Question: Determine the rms value of a semi-circular current wave which has a maximum value of a.

Options:

Answer:

Solution:

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