A sales rep used to work for a competitor. After a sales presentation, a prospect asks him, “Why should I choose your company over your competitor?” What should the rep do?
A thermocouple, which behaves as a first-order instrument, has a time constant of 16 ms. Determine its 90% rise time. Show answers using 3 significant digits minimum.
The Correct Answer and Explanation is :
1. What should the sales rep do when asked, “Why should I choose your company over your competitor?”
When a sales rep is asked this question, the goal is to emphasize the value and unique benefits their company provides while maintaining professionalism. Here’s what the rep should do:
- Focus on the company’s strengths: Highlight the features or services that make their company stand out. For example, better customer service, unique product features, more competitive pricing, or superior warranties.
- Avoid negative comparisons: It’s crucial to avoid directly criticizing the competitor. Negative comments may reflect poorly on the sales rep and the company. Instead, the rep should focus on their company’s strengths.
- Align the product to the prospect’s needs: The rep should relate the benefits of their product or service to the specific needs of the prospect. This requires listening to the prospect’s concerns and tailoring the pitch to show how the company’s solution is the best fit for the prospect’s unique situation.
- Use testimonials or success stories: If applicable, the sales rep can provide examples of other clients who have benefited from the company’s products or services. This can help build credibility and trust.
- Ask clarifying questions: To better address the prospect’s needs, the rep might ask what factors are most important to them in choosing a supplier (e.g., price, quality, service). This gives the rep a chance to customize their response.
2. Thermocouple Time Constant Calculation
For a thermocouple that behaves as a first-order instrument, the rise time is typically defined as the time it takes for the instrument’s output to rise to 90% of its final value after a step change in input. For a first-order system, the rise time can be approximated using the following formula:
[
t_{90} \approx 2.2 \cdot \tau
]
where:
- ( t_{90} ) is the 90% rise time,
- ( \tau ) is the time constant.
Given that the time constant ( \tau = 16 \, \text{ms} ), the 90% rise time can be calculated as:
[
t_{90} = 2.2 \times 16 \, \text{ms} = 35.2 \, \text{ms}
]
Thus, the 90% rise time for this thermocouple is approximately 35.2 ms.
Explanation:
The formula ( t_{90} \approx 2.2 \cdot \tau ) is derived from the exponential response of a first-order system. For first-order systems, the output response to a step input follows the equation:
[
y(t) = y_{\text{final}} \left( 1 – e^{-\frac{t}{\tau}} \right)
]
where ( y(t) ) is the output at time ( t ), and ( y_{\text{final}} ) is the final value of the output. At ( t = t_{90} ), the output reaches 90% of its final value, and the equation simplifies to the approximation ( t_{90} \approx 2.2 \cdot \tau ), which is a convenient rule for quick calculations.
For first-order instruments like this thermocouple, the 90% rise time provides insight into how quickly the system reacts to changes in input.