Janet installed a dimmer on the lights in her bedroom. She slid the dimmer switch up, causing the resistance in the circuit to decrease. Assuming the voltage is constant, what will Janet's actions have on the circuit?
Select all the correct answers.
A. The voltage will increase from 120 to 240 volts.
B. The lights will brighten.
C. The current will decrease.
D. The current will increase.
E. The lights will dim.
Answer (1)
Decreasing the resistance in the circuit increases the current.
An increase in current causes the lights to brighten.
Ohm's Law ( V = I R ) explains the relationship between voltage, current, and resistance.
Therefore, the lights will brighten, and the current will increase. The lights will brighten and the current will increase.
Explanation
Problem Analysis Let's analyze the problem. Janet installed a dimmer switch, which, when slid up, decreases the resistance in the circuit. The voltage is assumed to be constant. We need to determine what effect this has on the circuit.
Applying Ohm's Law We can use Ohm's Law, which states that Voltage (V) = Current (I) * Resistance (R), or V = I R . Since the voltage is constant, we can rearrange the formula to I = R V . This shows that current is inversely proportional to resistance when voltage is constant.
Determining the Change in Current Since the resistance R decreases and the voltage V is constant, the current I must increase.
Determining the Effect on the Lights An increase in current will cause the lights to brighten because the power dissipated by the lights increases (Power P = I 2 R ).
Conclusion Therefore, the correct answers are:
The lights will brighten.
The current will increase.
Examples
Dimmer switches in homes use the principle of variable resistance to control the brightness of lights. By increasing the resistance, the current flowing through the light bulb decreases, causing it to dim. Conversely, decreasing the resistance allows more current to flow, making the bulb brighter. This is a practical application of Ohm's Law, where voltage remains constant while resistance and current are adjusted to achieve the desired lighting level.
