https://file.aiquickdraw.com/mathbot/file/17298911370330asfch2j.jpg

Let's break down the problem based on the image you uploaded:

### Part (b):
- **Task**: Recalculate the current using a *practical digital multimeter* (Siglet SDM3055). 
- **Key information**: 
  - Use the internal input resistance of the digital multimeter in the calculations.
  - The internal resistance (R_in) of the Siglet multimeter in ammeter mode is given as **5Ω**.
  - You are to record this result in a table (Table 3.3, labeled "Calculated Value").
  
  To perform this calculation, you would:
  1. Identify the circuit configuration from Figure 3.6 (not provided in the image but assumed to be in the problem set).
  2. Use Ohm's Law \(I = \frac{V}{R}\), accounting for the resistance of the multimeter (5Ω) in series with the original circuit resistance.
  
  Assuming the original circuit has resistance \(R_{total}\) (without the multimeter), the new effective resistance would be:
  \[
  R_{new} = R_{total} + 5 \, \Omega
  \]
  The new current would be:
  \[
  I_{new} = \frac{V}{R_{new}}
  \]

### Part (c):
- **Task**: Calculate the **instrument error** of the multimeter in ammeter mode.
- **Key information**:
  - The internal resistance of the meter affects the current measurement. 
  - Instrument error is likely calculated as the difference between the current measured by an ideal ammeter (which assumes zero internal resistance) and the practical multimeter (which has internal resistance).
  
  To compute the error:
  \[
  \text{Error} = \frac{I_{ideal} - I_{new}}{I_{ideal}} \times 100 \%
  \]
  Where:
  - \(I_{ideal}\) is the current calculated assuming an ideal ammeter (zero internal resistance).
  - \(I_{new}\) is the current with the multimeter's internal resistance (as calculated in part b).

---

To proceed with the exact calculation, I would need the values of the voltage (\(V\)) and the original total resistance (\(R_{total}\)) from the circuit. Could you provide those, or clarify if they are part of the diagram in Figure 3.6?

Let me know if you'd like me to proceed with further details. 

### 5 Related Questions:
1. What is the value of the voltage (\(V\)) in the circuit as shown in Figure 3.6?
2. What is the original total resistance (\(R_{total}\)) of the circuit without the multimeter?
3. How do you think the multimeter's internal resistance affects current measurement accuracy?
4. Can you provide the full setup from Table 3.3 for clearer insight into the other parameters measured?
5. What is the full-scale deflection voltage mentioned in part (c) for the instrument error calculation?

### Tip:
When calculating error percentages, always ensure you use the exact values for \(I_{ideal}\) and \(I_{new}\) to avoid rounding errors.

b) Re-calculate the current if a practical digital multimeter (Siglet SDM3055) is used instead of an ideal meter as shown in Figure 3.6. Include the internal input resistance of the meter in your calculations. Record your results in the column labeled 'Calculated value' in Table 3.3 of the Lab Measurements Sheet. Rin for Siglet ammeter (multimeter) is approximately 5Ω. c) The internal resistance of meters in the ammeter mode can be calculated using the voltage drops at full-scale deflection obtained from the instrument specifications. Also, calculate and record in Table 3.3 the instrument error when using the digital ammeter.

Learn how to recalculate the current using a practical digital multimeter (Siglet SDM3055) by incorporating its internal resistance of 5Ω. This solution also covers the calculation of instrument error based on the internal resistance of the ammeter and the difference between ideal and practical measurements.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation