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In an experiment on Ohm's law, voltage drop across a resistor has been measured as V=(100+- 5) volt and current through the resistor has been measured as I=(10.0+-0.2) AMPERE. The permissible error in calculation of R IS?
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In an experiment on Ohm's law, voltage drop across a resistor has been...
Calculation of Permissible Error in Calculation of Resistance


  1. Ohm's Law

    2. Ohm's law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points. Mathematically, it can be expressed as:

    I = V/R


  2. Calculation of Resistance

    3. From Ohm's Law, the resistance can be calculated as:

    R = V/I


  3. Error in Calculation of Resistance

    4. The error in calculating resistance can be determined using the formula:

    Error in Resistance (δR) = |δV/V| + |δI/I|

    where δV is the error in voltage measurement and δI is the error in current measurement.


  4. Calculation of Permissible Error

    5. Given that:

    V = (100 - 5) V = 95 V

    I = (10.0 - 0.2) A = 9.8 A

    Let's assume that the error in voltage measurement is ±0.5 V and the error in current measurement is ±0.1 A.

    Substituting the values in the formula for error in resistance, we get:

    δR = |±0.5/95| + |±0.1/9.8|

    δR = 0.005 + 0.0102

    δR = 0.0152


  5. Permissible Error

    6. The permissible error in calculating the resistance is 0.0152 or 1.52%.

    Therefore, the calculated value of resistance should be within ±1.52% of the actual value.

Community Answer
In an experiment on Ohm's law, voltage drop across a resistor has been...
∆R/R = ∆ V/V + ∆ I / I
∆ R/ R = 5/100 + 0.2. / 1
∆ R = 10 ( 0.05 + 0.2)
= 10 × 0.25 = 2.5 Ohm
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In an experiment on Ohm's law, voltage drop across a resistor has been measured as V=(100+- 5) volt and current through the resistor has been measured as I=(10.0+-0.2) AMPERE. The permissible error in calculation of R IS?
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