Question

use the diagram and data table to answer the following question:

which statement is supported by the information provided?
a replacing the bulb with another motor will increase the current in the circuit because the motor requires more energy to spin.
b replacing the motor with another bulb will increase the current in the circuit because the motor has a greater resistance than the bulb.
c replacing the bulb with another motor will have no effect on the current in the circuit because all loads share the same current in a series circuit.
d replacing the motor with another bulb will have no effect on the current in the circuit because all loads share the same current in a series circuit.

Explanation:

Step1: Recall Ohm's Law and Series Circuit Properties

Ohm's Law is \(I=\frac{V}{R}\), where \(I\) is current, \(V\) is voltage, and \(R\) is resistance. In a series circuit, the total resistance \(R_{total}=R_1 + R_2+\cdots+R_n\).

Step2: Analyze Option A

If we replace the bulb (\(R = 50\space\Omega\)) with a motor (\(R = 100\space\Omega\)), the total resistance \(R_{total}\) increases. Using \(I=\frac{V}{R}\), when \(V = 3\space V\) (constant) and \(R\) increases, \(I\) decreases. So, option A is wrong.

Step3: Analyze Option B

The motor has \(R = 100\space\Omega\) and the bulb has \(R = 50\space\Omega\). If we replace the motor (\(R = 100\space\Omega\)) with a bulb (\(R = 50\space\Omega\)), the total resistance \(R_{total}\) decreases. Using \(I=\frac{V}{R}\), when \(V\) is constant (\(V=3\space V\)) and \(R\) decreases, \(I\) increases.

Step4: Analyze Option C

Replacing the bulb with a motor changes the resistance. Since \(I=\frac{V}{R}\), and \(V\) is constant (\(V = 3\space V\)), changing \(R\) (total resistance) will change \(I\). So, option C is wrong.

Step5: Analyze Option D

Replacing the motor with a bulb changes the resistance. Since \(I=\frac{V}{R}\), and \(V\) is constant (\(V = 3\space V\)), changing \(R\) (total resistance) will change \(I\). So, option D is wrong.

Answer:

B. Replacing the motor with another bulb will increase the current in the circuit because the motor has a greater resistance than the bulb.