Question

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

• A. both bulbs will glow alternatively
• B. both bulbs will glow with same brightness provided frequency $f =\frac{1}{2\pi\sqrt{\left(1/LC\right)}}$
• C. bulb $b_1$ will light up initially and goes off, bulb $b_2$ will be ON constantly
• D. bulb $b_1$ will blink and bulb $b_2$ will be ON constantly

Answer 1

Answer: (B)

At resonance both bulbs will glow with same brightness. At resonance, $X_{L}=X_{C}$
or $2 \pi f L=\frac{1}{2 \pi f C}$
or $f=\frac{1}{2 \pi \sqrt{L C}}$