Math Problem Statement
Solution
Let's go through the problem one by one.
Question 2(b)
The question refers to Figure 1, a circuit diagram used for measuring resistance , using an ammeter and a voltmeter. Here's a breakdown of the requested items:
Given:
- Ammeter reading (on a range)
- Voltmeter reading (on a range)
- Ammeter error:
- Voltmeter error:
- Ammeter resistance
To Find:
(i) Total systematic error in instrument readings
(ii) Measured value of resistor
(iii) True value of resistor
(iv) Percentage error in the value of
Step-by-step solutions:
-
Systematic error
For the ammeter:- Instrument range
- Error due to construction:
- Scale error: 0.1 of a scale Total error for the ammeter .
For the voltmeter:
- Instrument range
- Error due to construction:
- Scale error: 0.1 of a scale Total error for the voltmeter .
-
Measured value of the resistor
From Ohm's law: But we also need to correct for the ammeter resistance. -
True value of resistor
The true value should take into account the internal resistance of the ammeter: -
Percentage error in
The percentage error is calculated as:Substituting values:
Would you like me to calculate the errors more precisely?
Additional Questions:
- How do you calculate the total uncertainty in measurements with multiple sources of error?
- What is the significance of ammeter internal resistance in resistance measurements?
- How can measurement errors be minimized in electrical circuits?
- How does percentage error change with increasing voltmeter or ammeter range?
- Why is it important to consider both systematic and random errors in an experiment?
Tip:
When calculating measurement errors, always check if the instrument’s internal resistances (like that of an ammeter or voltmeter) need to be included in your calculations for more accurate results.
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Math Problem Analysis
Mathematical Concepts
Error Analysis
Ohm's Law
Percentage Error
Formulas
Ohm's Law: V = IR
Systematic Error: ΔV = (0.4% × V_range) + 0.1
Systematic Error: ΔI = (0.3% × I_range) + 0.1
Percentage Error: ((Measured Value - True Value) / True Value) × 100
Theorems
Ohm's Law
Suitable Grade Level
College Level (Engineering/Physics)
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