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A resistance is determined by voltmeter ammeter method. The voltmeter reads 100 V with a probable error of ±12 V and ammeter reads 10 A with a probable error of ±2 A. Determine the probable error in the computed value of resistance
  • a)
  • b)
  • c)
    2.33Ω
  • d)
    3.33Ω 
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A resistance is determined by voltmeter ammeter method. The voltmeter ...
We have resistance 
Weighted probable error in the resistance due to voltage is,

Weighted probable error in the resistance due to current is,

Probable error in computed resistance is,
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Most Upvoted Answer
A resistance is determined by voltmeter ammeter method. The voltmeter ...
±1 V and the ammeter reads 2 A with a probable error of ±0.01 A. Using the formula 𝑅=𝑉/𝐼, determine the resistance with its probable error.

Using the formula 𝑅=𝑉/𝐼, we can find the resistance as:

𝑅 = 100 V / 2 A = 50 Ω

To determine the probable error in resistance, we use the formula:

Probable error in 𝑅 = √[(∂𝑅/∂𝑉)² × (probable error in 𝑉)² + (∂𝑅/∂𝐼)² × (probable error in 𝐼)²]

Where ∂𝑅/∂𝑉 and ∂𝑅/∂𝐼 are the partial derivatives of resistance with respect to voltage and current, respectively. These partial derivatives can be found using the formula:

∂𝑅/∂𝑉 = 1/𝐼

∂𝑅/∂𝐼 = -𝑉/𝐼²

Substituting the given values, we get:

Probable error in 𝑅 = √[(1/2)² × (1 V)² + (-100/4)² × (0.01 A)²]

= √[0.25 + 2.5]

= √2.75

= 1.66 Ω (approx)

Therefore, the resistance with its probable error is:

𝑅 = 50 ± 1.66 Ω
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A resistance is determined by voltmeter ammeter method. The voltmeter reads 100 V with a probable error of ±12 V and ammeter reads 10 A with a probable error of ±2 A. Determine the probable error in the computed value of resistancea)4Ωb)6Ωc)2.33Ωd)3.33ΩCorrect answer is option 'C'. Can you explain this answer?
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