A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 V respectively. A second voltage V2, which is independent of V1, is measured 200 times and its average and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 + V1 + V2. Then the standard deviation of V3 in volts is ________
V1 = 100 ± 1.5 V
V2 = 150 ± 2 V
V3 = V1 + V2
Standard deviation in V3 will be
\({\sigma _{{V_3}}} = \sqrt {{{\left( {\frac{{\partial {V_3}}}{{\partial {V_1}}}} \right)}^2}\sigma _{{V_1}}^2 + {{\left( {\frac{{\partial {V_3}}}{{\partial {V_1}}}} \right)}^2}\sigma _{{V_2}}^2}\)
\(\frac{{\partial {V_3}}}{{\partial {V_1}}} = 1,\frac{{\partial {V_3}}}{{\partial {V_2}}} = 1\)
\({\sigma _{{v_3}}} = \sqrt {{{\left( 1 \right)}^2} \times {{\left( {1.5} \right)}^2} + {{\left( 1 \right)}^2} \times {{\left( 2 \right)}^2}}\)
\({\sigma _{{v_3}}} = 2.5\:V\)
Important Questions from Error Analysis
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