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IIT-JEE 2010 Paper 1 Offline

MCQ (Single Correct Answer)

An AC voltage source of variable angular frequency $$\omega$$ and fixed amplitude V0 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.

Explanation

Impedance of the circuit,

$$Z = \sqrt {{{({X_C})}^2} + {{(R)}^2}} = \sqrt {{{\left( {{1 \over {\omega C}}} \right)}^2} + {R^2}} $$

As $$\omega$$ increases, Z decreases.

Current in the circuit, $$I = {{{V_0}} \over Z}$$

When $$\omega$$ is increased, the impedance of the circuit decreases and the current through the bulb increases. Therefore the bulb glows brighter.

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