A quantity is given by where is the permittivity of free space, is a length, is a potential difference and is a time interval. The dimensional formula for is the same as that of [2001]

Question

A quantity $X$ is given by $ε_{0} L \frac{Δ V}{Δ t}$ where $ε_{0}$ is the permittivity of free space, $L$ is a length, $Δ V$ is a potential difference and $Δ t$ is a time interval. The dimensional formula for $X$ is the same as that of [2001]

Smart Achievers · Accepted Answer

(4)

$Capacitance, C = \frac{Δ q}{Δ V} = \frac{ε_{0} A}{L} \Rightarrow ε_{0} = \frac{(Δ q) L}{A (Δ V)}$

$∴$ $X = ε_{0} L \frac{Δ V}{Δ t} = \frac{(Δ q) L}{A (Δ V)} L \frac{Δ V}{Δ t}$

$= \frac{(Δ q)}{Δ V} \frac{L^{2}}{L^{2}} \frac{Δ V}{Δ t} = \frac{Δ q}{Δ t} = I (current)$

Solution

Q.
A quantity $X$ is given by $ε_{0} L \frac{Δ V}{Δ t}$ where $ε_{0}$ is the permittivity of free space, $L$ is a length, $Δ V$ is a potential difference and $Δ t$ is a time interval. The dimensional formula for $X$ is the same as that of [2001]

1 resistance

2 charge

3 voltage

4 current

Ans.
(4)

$Capacitance, C = \frac{Δ q}{Δ V} = \frac{ε_{0} A}{L} \Rightarrow ε_{0} = \frac{(Δ q) L}{A (Δ V)}$

$∴$ $X = ε_{0} L \frac{Δ V}{Δ t} = \frac{(Δ q) L}{A (Δ V)} L \frac{Δ V}{Δ t}$

$= \frac{(Δ q)}{Δ V} \frac{L^{2}}{L^{2}} \frac{Δ V}{Δ t} = \frac{Δ q}{Δ t} = I (current)$

Want Us to Email you About Special Offers & Updates?