2. Movie theater dimmers: In movie theater tl dim the lights by using variable inductor (i.e. the inductance value can be adjusted) connected to the bulbs. A light bulb is rated 120 V, 1000W, and is connected to the circuit as shown, domestic electrici 120 V 60 Hz. What must be the maximum inductance value if you want to dim the lights down to 1/5 of their intensity. What if instead of an induc you used a resistor what must be the value of the resistor to dim the lights down to 1/5. Ass the light bulb behaves like an ohmic resistor throughout. Note more than one steps are nee

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### Movie Theater Dimmers: 

In movie theaters, lights can be dimmed using a variable inductor (i.e., the inductance value can be adjusted) connected to the light bulbs. A light bulb is rated at 120 V, 1000 W, and is connected to the circuit as shown, using domestic electricity of 120 V at 60 Hz. 

**Problem:** Determine the maximum inductance value needed to dim the lights to 1/5 of their intensity. Additionally, if a resistor is used instead of an inductor, what must be the value of the resistor to achieve the same dimming effect? Assume the light bulb behaves as an ohmic resistor throughout. Note that more than one step is required to solve this problem.

**Answer:** 
- Maximum inductance: 76.4 mH
- Resistor value: 17.8 Ω

### Circuit Diagram Explanation:

- The diagram shows an AC power source connected in series with an inductor \( L \) and a light bulb. The inductor is represented by a coil symbol, and the light bulb is shown as a filament bulb. 
- An arrow across the inductor suggests its varying (adjustable) inductance capability, which is used to control the brightness of the bulb.
Transcribed Image Text:### Movie Theater Dimmers: In movie theaters, lights can be dimmed using a variable inductor (i.e., the inductance value can be adjusted) connected to the light bulbs. A light bulb is rated at 120 V, 1000 W, and is connected to the circuit as shown, using domestic electricity of 120 V at 60 Hz. **Problem:** Determine the maximum inductance value needed to dim the lights to 1/5 of their intensity. Additionally, if a resistor is used instead of an inductor, what must be the value of the resistor to achieve the same dimming effect? Assume the light bulb behaves as an ohmic resistor throughout. Note that more than one step is required to solve this problem. **Answer:** - Maximum inductance: 76.4 mH - Resistor value: 17.8 Ω ### Circuit Diagram Explanation: - The diagram shows an AC power source connected in series with an inductor \( L \) and a light bulb. The inductor is represented by a coil symbol, and the light bulb is shown as a filament bulb. - An arrow across the inductor suggests its varying (adjustable) inductance capability, which is used to control the brightness of the bulb.
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