Question

An AC voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $\omega$ is increased:

• A. The bulb glows dimmer
• B. The bulb glows brighter
• C. Total impedance of the circuit is unchanged
• D. Total impedance of the circuit increases

Answer 1

The correct option is B

The bulb glows brighter

Explanation for Correct Option:

Option B

1. Impedance(Z) the measure of the total opposition that is made by a circuit towards the flow of current through it.
2. It is given by the formula, $Z=\sqrt{\frac{1}{{\left(\omega C\right)}^2}+R^2}$.
3. Clearly, impedance is inversely proportional to angular frequency, $Z\propto \sqrt{\frac{1}{\omega }}$.
4. If angular frequency increases, the impedance will decrease. Therefore, the opposition to the current will be less and the bulb will glow brightly.

Explanation for Incorrect Options:

Option A:

The bulb will be dimmer if impedance increases, but since frequency increases impedance will decrease and the bulb will glow dimmer.

Option C:

As the frequency increases impedance will change.

Option D:

If angular frequency increases, the impedance will decrease and not increase.

Thus, option (B) is correct.