A galvanometer has a coil of resistance $100 \Omega$ showing a full scale deflection at $50 \mu \mathrm{A}$.…

A galvanometer has a coil of resistance $100 \Omega$ showing a full scale deflection at $50 \mu \mathrm{A}$. The resistance that should be added to use it as an ammeter of range $10 \mathrm{~mA}$ is
  1. $5 \Omega$
  2. $5 \times 10^{-2} \Omega$
  3. $0.5 \Omega$
  4. $1 \Omega$

Solution

Given, Resistance of galvanometer $ \begin{aligned} R_g & =100 \Omega \\ I_g & =50 \mu \mathrm{A}=5 \times 10^{-5} \mathrm{~A} \\ I & =10 \mathrm{~mA}=10^{-2} \mathrm{~A} \\ R_s & =? \end{aligned} $ We know that, $ R_s=\frac{I_g}{I-I_g} \times R_g . $ $\begin{aligned} & =\frac{5 \times 10^{-5}}{10^{-2}-5 \times 10^{-5}} \times 100 \\ & =\frac{5 \times 10^{-3}}{(1000-5) 10^{-5}}=\frac{5 \times 10^2}{995} \\ & =\frac{500}{995}=0.503 \\ & \simeq 0.5 \Omega\end{aligned}$

Asked in: AP EAMCET 2022 (06 Jul Shift 2)

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