Question

A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillation of frequency f. If L is doubled and C is changed to 4C, the frequency will be ____________.

Options

• `"f"  2sqrt2`

• f / 2

• f / 4

• 8f

Answer 1

A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillation of frequency f. If L is doubled and C is changed to 4C, the frequency will be `"f"  2sqrt2`.

Explanation:

`"f"_r = 1/(2pi sqrt"LC") Rightarrow "f"_r prop 1/sqrt("LC")`

`therefore ("f"_r)_2/("f"_r)_1 = 1/sqrt("L"_2 "C"_2) sqrt("L"_1"C"_1) = (("L"_1 "C"_1)/("L"_2 "C"_2))^(1/2)`

`= ("L" xx "C")/(2"L" xx 4"C")^(1/2)`

`= 1/(8)^(1/2)`

`therefore ("f"_r)_2/("f"_r)_1 = 1/(2sqrt2)`

`("f"_r)_2 = "f"_1/(2sqrt2)`

`therefore ("f"_r)_2 = "f"/(2sqrt2)   .....[because ("f"_r)_1 = "f"]`