# Comparing two circuits with an AC source

• mb85
However, in steady state, the bulb in the second circuit can only be as bright as the bulb in the first circuit if the inductor and capacitor are at resonance. Otherwise, the power factor will be less than one and the actual power delivered to the bulb will be less. In summary, the brightness of the bulb in the second circuit can only match that of the first circuit if the inductor and capacitor are at resonance, otherwise it will be less due to a lower power factor. It is not possible for the bulb in the second circuit to be brighter than the first circuit in steady state.
mb85

## Homework Statement

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.

## 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?

mb85 said:
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?

mb85 said:
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?

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.

SGT said:
In steady state the brightness of the bulb is identical with or without the RC circuit.
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.

antonantal said:
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.

## 1. How do you compare the voltage and current in two circuits with an AC source?

To compare the voltage and current in two circuits with an AC source, you can use a multimeter to measure the voltage and current at various points in each circuit. Make sure to use the same settings on the multimeter for both circuits to ensure accurate comparisons.

## 2. What is the difference between series and parallel circuits in terms of AC source?

In a series circuit, the components are connected one after another, with the same current flowing through each component. In a parallel circuit, the components are connected to the same two points, with the voltage across each component being the same. When comparing the two circuits with an AC source, the total voltage and current will be the same in a series circuit, while the voltage and current will vary in a parallel circuit.

## 3. How do you analyze the phase difference between two circuits with an AC source?

The phase difference between two circuits with an AC source can be analyzed by measuring the voltage and current at the same point in each circuit, and then calculating the phase angle using the formula phase angle = arctan (voltage/current).

## 4. Why is it important to compare two circuits with an AC source?

Comparing two circuits with an AC source can help determine which circuit is more efficient, which components are causing a greater voltage drop, and which circuit is better suited for a specific application. It can also help identify any inconsistencies or issues in the circuits that may need to be addressed.

## 5. Can two circuits with the same components have different behaviors when connected to an AC source?

Yes, even with the same components, two circuits can have different behaviors when connected to an AC source. This can be due to the layout and arrangement of the components, the type of connections used, or any external factors such as environmental conditions. It is important to compare the two circuits to fully understand their behaviors and make any necessary adjustments for optimal performance.

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