Which of the following dimensions will be the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The dimension of resistance $R$ is $[M L^2 T^{-3} I^{-2}]$.The dimension of inductance $L$ is $[M L^2 T^{-2} I^{-2}]$.The dimension of capacitance

Vedclass · Accepted Answer

$\frac{L}{R}$

Vedclass · Answer

(B) The dimension of resistance $R$ is $[M L^2 T^{-3} I^{-2}]$.The dimension of inductance $L$ is $[M L^2 T^{-2} I^{-2}]$.The dimension of capacitance $C$ is $[M^{-1} L^{-2} T^4 I^2]$.Checking option $B$:$\frac{L}{R} = \frac{[M L^2 T^{-2} I^{-2}]}{[M L^2 T^{-3} I^{-2}]} = [T^1] = T$.Checking option $C$:$\sqrt{LC} = \sqrt{[M L^2 T^{-2} I^{-2}] \cdot [M^{-1} L^{-2} T^4 I^2]} = \sqrt{[T^2]} = [T^1] = T$.Since both $B$ and $C$ result in the dimension of time,the question implies identifying expressions with time dimensions. Given the standard format,both $\frac{L}{R}$ and $\sqrt{LC}$ are correct.

Which of the following dimensions will be the same as that of time?

Similar Questions

The impedance of an $LR$ circuit with $L=\frac{60}{\pi} \text{ mH}$,$R=8 \Omega$ and frequency $f=50 \text{ Hz}$ is (in $\Omega$)

In a series $LCR$ circuit, the $rms$ voltage across the resistor and the capacitor are $30 \ V$ and $90 \ V$ respectively. If the applied voltage is $V = 50 \sqrt{2} \sin \omega t$, then the peak voltage across the inductor is

When an $AC$ source of emf $E$ with angular frequency $\omega = 100 \text{ rad/s}$ is connected across a circuit, the phase difference between $E$ and current $I$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the figure. If the circuit consists of only $RC$ or $RL$ in series, then:

If $E = 200\,V$,$R = 25\,\Omega$,$L = 2\,H$,and $C = 2\,\mu F$ and the frequency is variable,then the current at $f = 0$ and $f = \infty$ will be respectively:

In the circuit shown below,the $ac$ source has voltage $V = 20\cos (\omega t)$ volts with $\omega = 2000 \,rad/sec$. The amplitude of the current will be nearest to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module