Galvanometer calibration by half deflection ($R_g=RS/(R-S)$)

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. ^[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 currentsIf 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. ^[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.