A team of plasma physicists conducted an experiment to investigate electrical breakdown ph… — ACT

A team of plasma physicists conducted an experiment to investigate electrical breakdown phenomena in synthetic atmospheric gas mixtures. In a sealed dielectric chamber, researchers systematically varied the volume ratio of nitrogen ( $N_2$ ) to oxygen ( $O_2$ ) across ten trials while recording the threshold breakdown voltage ( $V_{bd}$ ) required to initiate a spark discharge. Throughout all experimental trials, the spacing between the two planar copper electrodes was fixed at $5.0\text{ mm}$ , the total cell pressure was held constant at $101.3\text{ kPa}$ , and the ambient temperature was maintained at $298\text{ K}$ .

Match each experimental component from this investigation to its correct variable classification.

Volume ratio of $N_2$ to $O_2$ Independent Variable (manipulated parameter)
Threshold breakdown voltage ( $V_{bd}$ )Dependent Variable (measured outcome)
Electrode spacing distance ( $5.0\text{ mm}$ )Controlled Variable (apparatus geometry parameter)
Total cell pressure ( $101.3\text{ kPa}$ )Controlled Variable (thermodynamic condition parameter)

Answer

Volume ratio of

N_2

O_2

matches Independent Variable (manipulated parameter); Threshold breakdown voltage (

V_{bd}

) matches Dependent Variable (measured outcome); Electrode spacing distance (

5.0\text{ mm}

) matches Controlled Variable (apparatus geometry parameter); Total cell pressure (

101.3\text{ kPa}

) matches Controlled Variable (thermodynamic condition parameter).

In experimental design, the independent variable is the factor intentionally varied by experimenters (the ratio of

N_2

O_2

), while the dependent variable is the measured output that changes in response (the threshold breakdown voltage

V_{bd}

). Parameters held uniform throughout all trials to maintain experimental integrity are controlled variables, where electrode spacing standardizes apparatus geometry and chamber pressure standardizes ambient thermodynamic conditions.

Step-by-Step Solution

Identify the factor systematically changed by the researchers across experimental trials.

The researchers explicitly varied the volume ratio of

N_2

O_2

, identifying it as the independent variable.

The independent variable is the condition purposefully manipulated by the experimenter to observe its effect.

Identify the factor measured to evaluate the outcome of the experiment.

The threshold breakdown voltage (

V_{bd}

) is recorded in response to changes in gas composition, making it the dependent variable.

The dependent variable represents the response or yield measured as the experimental output.

Identify the parameters held constant during the experiment and differentiate their physical nature.

Electrode spacing (

5.0\text{ mm}

) controls the physical setup/geometry, while total pressure (

101.3\text{ kPa}

) controls the ambient thermodynamic environment.

Controlled variables must remain constant across all trials to prevent confounding influence on the dependent variable.

Key Concept

Distinguishing between independent variables (manipulated inputs), dependent variables (observed outcomes), and controlled variables (standardized conditions) in experimental design.

Estimated Time:2m 0s

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