SATHEE: Electro Magnetic Induction And Alternating Currents Question 197

Electro Magnetic Induction And Alternating Currents Question 197

Question: An ac source of angular frequency co is fed across a resistor R and a capacitor C in series. The current registered is I. If now the frequency of source is changed to $ω / 3$ (but maintaining the same voltage), the current in the circuit is found to be halved. Then the ratio of reactance to resistance at the original frequency $ω$ is

Options:

A) $\sqrt{3 / 5}$

B) $\sqrt{5 / 3}$

C) $\sqrt{2 / 3}$

D) $\sqrt{3 / 2}$

Show Answer

Answer:

Correct Answer: A

Solution:

According to given problem,

$I, = \frac{V}{Z}, = \frac{V}{{[R^{2} + {(1 / C ω)}^{2}]}^{1 / 2}}$ …(i) and

$\frac{I}{2}, = \frac{V}{{[R^{2} + {(3 / C ω)}^{2}]}^{1 / 2}}$ …(ii) Substituting the value of I from eq. (i) in (11),

$4, (R^{2} + \frac{1}{C^{2} ω^{2}}) = R^{2} + \frac{9}{C^{2}, ω^{2}}$ i.e.,

$\frac{1}{C^{2}, ω^{2}}, = \frac{3}{5}, R^{2}$ so that $\frac{X}{R}$

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Electro Magnetic Induction And Alternating Currents Question 197

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