Question

the diagram shows a simple circuit. which change would cause the lightbulb to get dimmer? a. swap the positions of the battery and the lightbulb. b. increase the length of the wire between the lightbulb and the battery. c. decrease the length of the wire between the switch and the battery. d. move the battery from the bottom to the right side.

Explanation:

Step1: Recall Ohm's Law and power - current relationship

The power dissipated in a light - bulb is $P = I^{2}R$, where $I$ is the current through the bulb and $R$ is the resistance of the bulb. To make the bulb dimmer, we need to decrease the current flowing through it. According to Ohm's Law $I=\frac{V}{R_{total}}$, where $V$ is the voltage of the battery and $R_{total}$ is the total resistance of the circuit.

Step2: Analyze the effect of each option on resistance

• Option A: Swapping the positions of the battery and the light - bulb does not change the total resistance of the circuit, so the current and the brightness of the bulb remain the same.
• Option B: Increasing the length of the wire between the light - bulb and the battery increases the total resistance of the circuit ($R=

ho\frac{l}{A}$, where $
ho$ is the resistivity of the wire material, $l$ is the length of the wire, and $A$ is the cross - sectional area of the wire). As $R_{total}$ increases, according to $I = \frac{V}{R_{total}}$, the current $I$ decreases. Since $P=I^{2}R$ (where $R$ of the bulb is constant), a decrease in $I$ leads to a decrease in power dissipated in the bulb, making it dimmer.

• Option C: Decreasing the length of the wire between the switch and the battery decreases the total resistance of the circuit. According to $I=\frac{V}{R_{total}}$, the current increases, and the bulb gets brighter.
• Option D: Moving the battery from the bottom to the right - hand side does not change the total resistance of the circuit, so the current and the brightness of the bulb remain the same.

Answer:

B. Increase the length of the wire between the lightbulb and the battery.