Question

In the circuit shown in figure, if both the bulbs $B_1$ and $B_2$ are identical:

• A. Only $B_2$ will glow because the capacitor has infinite impedance
• B. Their brightness will be the same
• C. $B_2$ will be brighter than $B_1$
• D. As frequency of supply voltage is increased , the brightness of bulb $B_1$ will increase and that of $B_2$ will decrease.

Answer 1

The correct option is C $B_2$ will be brighter than $B_1$

Bulb acts as a resistor in circuit.

Therefore, $I_C=\frac{E}{\sqrt{R^2+{\left(\frac{1}{\omega C}\right)}^2}}$

From the given diagram, $X_C=\frac{1}{C\omega }=\frac{20}{\pi }\Omega$

Brightness of $B_1=I_C^{2}R$

And , $I_L=\frac{E}{\sqrt{R^2+(\omega L{)}^2}}$

From the given diagram, $X_L=L\omega =10\times {10}^{-3}\times 2\pi \times 50=\pi \Omega$

Thus, $X_C>X_L\Rightarrow I_L>I_C$

Therefore, $B_2$ will be brighter.

Hence, option (b) is the correct answer.