Question

L, C and R represents inductance, capacitance and resistance respectively. The combinations that have the dimensions of frequency are :

• A. $\frac{1}{CR}$
• B. $\frac{R}{L}$
• C. $\frac{1}{\sqrt{LC}}$
• D. All of the above

Answer 1

The correct option is D All of the above

We know that unit for the frequency is per second i.e.$[T{]}^{-1}$

Now let us consider the dimensions of the given physical quantities.

We know that Capacitance i.e.

$C=Q/V$

where Q is electric charge and V is electric potential.

Now we know that Q= It where I is current and t is time.

Also that V=IR where R is resistance.

So,

$C=It/IR$

Thus,

$C=t/R$

also $1/t=1/RC$

Thus dimension of $1/RC$ will be $\left[T^{-1}\right]$ that is same as that of frequency.

Now Inductance(L) can be given as

$L=Vt/I$

And also $V=IR$

Therefore $L=IRt/I$

Thus, $R/L=1/t$

It means both A and B are correct now checking for the third option

$LC=Rt\ast t/R=t^2$

That gives $1/\sqrt{LC}=1/t$

Thus dimension of $1/\sqrt{LC}$ will be $T^{-1}$ that is same as that of frequency.