General Physics Ques 15
- In terms of potential difference $V$, electric current $I$, permittivity $\varepsilon_0$, permeability $\mu_0$ and speed of light $c$, the dimensionally correct equations is/are
(2015 Adv.)
(a) $\mu_0 I^2=\varepsilon_0 V^2$
(b) $\varepsilon_0 I=\mu_0 V$
(c) $I=\varepsilon_0 c V$
(d) $\mu_0 c I=\varepsilon_0 V$
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Answer:
Correct Answer: 15.( a, c )
Solution:
- (a) Energy of inductor $\frac{1}{2} \mathrm{LI}^2=\frac{1}{2} \frac{\mu_0 N^2 A}{l} I^2$
Energy of capacitor $=\frac{1}{2} C V^2=\frac{1}{2} \varepsilon_0 \frac{A}{d} V^2$
$\mu_0 \frac{A}{l} I^2$ and $\varepsilon_0 \frac{A}{d} V^2$ have same dimension.
So, $\mu_0 I^2$ and $\varepsilon_0 V^2$ have same dimension.
(c) $Q=C V, \frac{Q}{t}=\frac{C V}{t}$
$I=\varepsilon_0 \frac{A}{l} \frac{V}{t} \frac{A}{l t}$ have unit of speed.
So, $\quad I=\varepsilon_0 c V$
BETA
