First slide

AC Circuits

Question

Two identical incandescent light bulbs are connected as shown in the figure. When the circuit is connected to an AC voltage source of frequency f, which of the following
observations will be correct?

Moderate

A

Both bulbs will glow alternatively
B

Both bulbs will glow with same brightness provided frequency, $f = \frac{1}{2 π} \sqrt{(\frac{1}{L C})}$
C

Both $b_{1}$ will light up initially and goes off, bulb $b_{2}$ will be on constantly
D

Both $b_{1}$ will blink and $b_{2}$ will be on constantly

Solution

Both bulbs will glow with same brightness if
$X_{L} = X_{C} (∵ X_{L} = ω L) (∵ ω = 2 π f)$
2. $X_{c} = \frac{1}{ω C}$
The condition shown above ensures the same current in both bulbs.
On simplifying we get,
$2 π f L = \frac{1}{2 π f C}$
$o r f = \frac{1}{2 π \sqrt{L C}}$
Therefore, the correct answer is (B).

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