An AC voltage source of variable angular frequency and fixed amplitude is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When is increased [2010]

Question

An AC voltage source of variable angular frequency $ω$ and fixed amplitude $V_{0}$ is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $ω$ is increased [2010]

Smart Achievers · Accepted Answer

(2)

$I_{rms} = \frac{V_{rms}}{Z} = \frac{V_{rms}}{\sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}}$

As $ω$ increases, $I_{rms}$ through the bulb increases. Hence the bulb glows brighter.

Solution

Q.
An AC voltage source of variable angular frequency $ω$ and fixed amplitude $V_{0}$ is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $ω$ is increased [2010]

1 the bulb glows dimmer

2 the bulb glows brighter

3 total impedance of the circuit is unchanged

4 total impedance of the circuit increases

Ans.
(2)

$I_{rms} = \frac{V_{rms}}{Z} = \frac{V_{rms}}{\sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}}$

As $ω$ increases, $I_{rms}$ through the bulb increases. Hence the bulb glows brighter.

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