JEE Advanced 2015 · Paper 2 · Physics Q10

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PhysicsMultiple correct+4 / -2Question 10 of 60

In terms of potential difference $V$ , electric current $I$ , permittivity $\varepsilon_0$ , permeability $\mu_0$ and speed of light $c$ , the dimensionally correct equation(s) is(are)

\mu_0I^2=\varepsilon_0V^2

\varepsilon_0I=\mu_0V

I=\varepsilon_0cV

\mu_0cI=\varepsilon_0V

Answer and worked solution

Official answer: A, C

Two useful facts. $\sqrt{\mu_0/\varepsilon_0}$ has the dimensions of resistance ( $V/I$ ), and $\varepsilon_0c=\sqrt{\varepsilon_0/\mu_0}$ .

(A) $\dfrac{V^2}{I^2}=\dfrac{\mu_0}{\varepsilon_0}$ . Correct.
(C) $\dfrac IV=\varepsilon_0c$ , the inverse of a resistance. Correct.
(B), (D) These give $V/I=\varepsilon_0/\mu_0$ or $\mu_0c/\varepsilon_0$ , which are not resistances.

(A), (C)

Topics:Dimensional analysis Properties of EM waves

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JEE Advanced 2015 · Paper 2, Physics question 10