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Error in sum of the quantities

Suppose x = a + b, i.e., sum of a and b.
 
Let
Δa = absolute error in measurement of a
Δb = absolute error in measurement of b
Δx = absolute error in calculation of x
 
Maximum absolute error in x is Δx = ±(Δa + Δb)
 
Percentage error in the value of
 
29795.png

Error in difference of the quantities

Suppose x = a – b
 
Let
Δa = absolute error in measurement of a
Δb = absolute error in measurement of b
Δx = absolute error in calculation of x, i.e., difference of a and b.
 
Maximum absolute error in x is Δx = ±(Δa + Δb)
 
Percentage error in the value of x is
 
29789.png

Error in product of quantities

Suppose x = a × b
 
Let
Δa = absolute error in measurement of a,
Δb = absolute error in measurement of b
Δx = absolute error in calculation of x, i.e., product of a and b.
 
Maximum fractional error in x is
 
29783.png
 
Percentage error in the value of x
= (% error in value of a) + (% error in value of b)

Error in division of quantities

Suppose x = a/b
 
Let
Δa = absolute error in measurement of a,
Δb = absolute error in measurement of b
Δx = absolute error in calculation of x, i.e.,division of a and b.
 
Maximum fractional error in x is
29771.png
 
Percentage error in the value of x
= (% error in value of a) + (% error in value of b)

Error in quantity raised to some power

Suppose x = an/bm.
 
Let
Δa = absolute error in measurement of a,
Δb = absolute error in measurement of b
Δx = absolute error in calculation of x
 
The maximum fractional error in x is
29759.png
 
Percentage error in the value of x
n (% error in value of a) + m (% error in value of b)

Some Important Applications

  • For a simple pendulum,
     
    30785.png
  • For a sphere
     
    30779.png
     
     30773.png and 30766.png
  • When two resistors R1 and R2 are connected
     
    In series Rs = R1 + R2
     
     ΔRs = ΔR1 + ΔR2
     
    30760.png
     
    In parallel,
     
    30754.png
     
     30748.png




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