Q. A galvanometer has a current sensitivity of $1\, mA$ per division. A variable shunt is connected across the galvanometer and the combination is put in series with a resistance of $500 \Omega$ and cell of internal resistance $1 \Omega$. It gives a deflection of 5 division for shunt of $5$ ohm and $20$ division for shunt of $25$ ohm. The emf of cell is
Solution:
Here, $I=\frac{E}{R+r+\frac{GS}{G+S}}$ and $I_{g}=\frac{IS}{G+S}$
$I_{g}=\frac{E}{\left(R+r\right)+\frac{GS}{\left(G+S\right)}}\times\frac{S}{\left(G+S\right)}$
$\therefore I_{g}=\frac{ES}{\left(R+r\right)\left(G+S\right)+GS}$
For $S = 5 \,$ohm, $I_{g} = 5 × 10^{-3} A$ and for $S = 25\,$ ohm,
$I_{g}=20\times10^{-3} $A
Hence, $5 \times10^{-3}=\frac{E\times5}{501\left(G+25\right)+5G}...\left(i\right)$
and $20\times10^{-3}=\frac{E\times5}{501\left(G+5\right)+25G} ...\left(ii\right)$
Dividing and solving,
$G = 88.2\, \Omega$
From $\left(i\right), $we get
$E = 10^{-3} \left[501 \left(88.2 + 5\right) + 5 × 88.2\right]$
$\,= 47.1 \, volt$
