= Galvanometer calibration by half deflection
{title2=$R_g=RS/(R-S)$}
NCERT's teaching experiment uses a <moving-coil galvanometer>, a 0–6 V supply, a 0–10 kΩ series <electrical resistance> box $R$, a 0–200 Ω parallel <electrical resistance> box $S$, two switches and a <voltmeter>. With the parallel path open, close the supply switch and record the pointer deflection. Keep $R$ fixed, close the parallel path, and adjust $S$ until the deflection halves. The guide requests repeated settings, clean tight contacts and constant supply <electromotive force>; it introduces high $R$ before energizing to protect the winding. <Laboratory Manual Physics, Class XII/Experiment 6: Resistance and figure of merit of a galvanometer>[Experiment 6, printed pp. 53–58: Figure E 6.1, Procedure 1–5, Precautions and Sources of Errors]{ref}
Write the winding <electrical resistance> as $R_g$, the supply <electromotive force> as $E$, and assume negligible supply internal <electrical resistance>. <Ohm's law> gives the two winding <electric currents>
$$
I_1=\frac{E}{R+R_g},\qquad I_2=\frac{ES}{R(R_g+S)+R_gS}.
$$
If proportional deflection gives $I_2=I_1/2$, solving yields $R_g=RS/(R-S)$, requiring $R>S$. The shortcut $R_g\simeq S$ requires $R\gg R_g$; closing the parallel path generally changes the total supply <electric current>. For chosen values $R=9900\,\Omega$ and $S=99.0\,\Omega$, the exact result is $R_g=100\,\Omega$, rather than $99\,\Omega$. The manual gives this exact relation and asks how finite supply internal <electrical resistance> affects it. <Laboratory Manual Physics, Class XII/Experiment 6: Resistance and figure of merit of a galvanometer>[Experiment 6, printed pp. 54–55, equations (E 6.2), (E 6.8) and (E 6.9); p. 58, Self Assessment 4]{ref}
As an additional calibration control, record the supply-off zero, apply several small positive and negative <electric currents>, and recheck zero after each sequence. With $R_g$ known, calculate each <electric current> from the measured supply <electric potential difference> and the total series <electrical resistance>; plot settled deflection against that <electric current>. Equal-magnitude reversed readings should lie equally far from a stable zero. A fitted relation $\theta_{\mathrm{read}}=\theta_0+S_I I$ separates zero offset from <galvanometer current sensitivity>. The manual's “figure of merit” is <electric current> per scale division, not the mechanical <torsional spring constant> $k$ used above. These reversal and zero checks extend the documented procedure; they are proposed controls, not reported measurements.
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