Question

Two ammeters $A_1$ and $A_2$ measure the same current and provide readings $I_{1}and{I}_2,$ respectively. The ammeter errors can be characterized as independent zero mean Gaussian random variable of standard deviations ${\sigma }_{1}and{\sigma }_2,$ respectively. The value of the current is computed as:

$I=\mu I_1+(1-\mu )I_2$

The value of $\mu$ which gives the lowest standard deviation of I is

• A. $\frac{{\sigma }_2^2}{{\sigma }_1^2+{\sigma }_2^2}$
• B. $\frac{{\sigma }_1^2}{{\sigma }_1^2+{\sigma }_2^2}$
• C. $\frac{{\sigma }_2}{{\sigma }_1+{\sigma }_2}$
• D. $\frac{{\sigma }_1}{{\sigma }_1+{\sigma }_2}$

Answer 1

The correct option is A $\frac{{\sigma }_2^2}{{\sigma }_1^2+{\sigma }_2^2}$

$\frac{{\sigma }_2^2}{{\sigma }_1^2+{\sigma }_2^2}$