NEET-XII-Physics
38: Electromagnetic Induction
- #9L, C and R represent the physical quantities inductance, capacitance and resistance respectively. Which of the following combinations have dimensions of frequency?
(a)
1RC
(b)
RL
(c)
1LC
(d) C/L.digAnsr: a,b,cAns : (a) `` \frac{1}{RC}``
(b) `` \frac{R}{L}``
(c) `` \frac{1}{\sqrt{LC}}``
The time constant of the RC circuit is given by
`` \tau =RC``
On taking the reciprocal of the above relation, we get
`` {f}_{1}=\frac{1}{RC}`` ...(1)
f1 will have the dimensions of the frequency.
The time constant of the LR circuit is given by
`` \tau =\frac{L}{R}``
On taking the reciprocal of the above relation, we get
`` {f}_{2}=\frac{R}{L}`` ...(2)
f2 will have the dimensions of the frequency.
On multiplying eq. (1) and (2), we get
`` {f}_{1}{f}_{2}=\frac{1}{LC}``
`` \Rightarrow \sqrt{{f}_{1}{f}_{2}}=\frac{1}{\sqrt{LC}}``
Thus, `` \sqrt{{f}_{1}{f}_{2}}`` will have the dimensions of the frequency.
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