# Comparing two circuits with an AC source

#### mb85

1. The problem statement, all variables and given/known data
The problem says.
Shown are two circuits. In one circuit, a light bulb is connected directly to an AC source. In the second circuit, an identical light bulb is connected in series with an inductor and a capacitor to an identical AC source.

a- is it possible for the bulb in the second circuit to be as bright as the bulb in the first circuit? explain.
b- is it possible for the bulb in the second circuit to be brighter than the bulb in the first circuit? explain.

2. Relevant equations

3. The attempt at a solution
I know that the light bulbs can act as a resistor, but in the second circuit, does the capacitor over a certain amount of time not make the bulb as bright? In AC circuits the inductors, resistors and capacitors all act differently than in DC circuits but how does that effect the brightness?

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#### antonantal

is it possible for the bulb in the second circuit to be as bright as the bulb in the first circuit? explain.
Do you know what resonance is in a RLC circuit?

is it possible for the bulb in the second circuit to be brighter than the bulb in the first circuit? explain.
What would be required for the bulb in the second circuit to be brighter than the bulb in the first circuit?

S

#### SGT

Since inductors and capacitors don't dissipate energy, all energy provided by the source must be dissipated at the light bulb. In steady state the brightness of the bulb is identical with or without the RC circuit.
During the transient it is possible that the brightness of the bulb becomes greater or lower than in steady state.

#### antonantal

In steady state the brightness of the bulb is identical with or without the RC circuit.
Are you sure about that?
My answer would be that the bulb in the second circuit will be as bright as the bulb in the first circuit only if the inductor and the capacitor have the same reactance at the frequency of the AC source. This way the impedances of the inductor and the capacitor will cancel each other and the RLC circuit formed by the bulb the inductor and the capacitor will be at resonance (purely resistive).
Otherwise the power factor will be less than one, so although the source may be loaded the same, the actual power delivered to the bulb will be just a fraction of the power given by the source.

As for the second question i don't think that it is possible for the bulb in the second circuit to be brighter than the bulb in the first one, since this would require that the amplitude of the voltage drop across the bulb to be greater than the amplitude of the voltage given by the AC source.

S

#### SGT

As for the second question i don't think that it is possible for the bulb in the second circuit to be brighter than the bulb in the first one, since this would require that the amplitude of the voltage drop across the bulb to be greater than the amplitude of the voltage given by the AC source.
This is possible during the transient.

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