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Two resistors with nominal resistance values $R_{1}$ and $R_{2}$ have additive uncertainties $\bigtriangleup R_{1}$ and $\bigtriangleup R_{2}$, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance $R$ is

  1. $\pm \sqrt{\left \{ \frac{\partial R}{\partial R_{1}}\bigtriangleup R_{1} \right \}^{2}+\left \{ \frac{\partial R}{\partial R_{2}}\bigtriangleup R_{2} \right \}^{2}}$
  2. $\pm \sqrt{\left \{ \frac{\partial R}{\partial R_{2}}\bigtriangleup R_{1} \right \}^{2}+\left \{ \frac{\partial R}{\partial R_{1}}\bigtriangleup R_{2} \right \}^{2}}$
  3. $\pm \sqrt{\left \{ \frac{\partial R}{\partial R_{1}} \right \}^{2}\bigtriangleup R_{2}+\left \{ \frac{\partial R}{\partial R_{2}} \right \}^{2}\bigtriangleup R_{1}}$
  4. $\pm \sqrt{\left \{ \frac{\partial R}{\partial R_{1}} \right \}^{2}\bigtriangleup R_{1}+\left \{ \frac{\partial R}{\partial R_{2}} \right \}^{2}\bigtriangleup R_{2}}$
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