Galvanometer: Figure of Merit
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flagWhat you'll discover
- arrow_forwardDefine figure of merit k = I/θ and current sensitivity
- arrow_forwardVary the series resistance and record deflections
- arrow_forwardCompute k = E/(R + G)θ for each setting and average
- arrow_forwardCalculate the current Ig for full-scale deflection
What the figure of merit means
A moving-coil galvanometer deflects in proportion to the current through its coil: θ divisions for current I, with k = I/θ the figure of merit — the current needed per division of deflection. A typical school galvanometer has k around 10⁻⁵ A/div: a 30-division scale therefore reaches full deflection at Ig = 30k, well under a milliamp.
Knowing k is the gateway to building real meters: converting the galvanometer to an ammeter needs a shunt resistance carrying everything beyond Ig, and converting to a voltmeter needs a high series resistance. Both calculations begin with the k you measure here.
Circuit and calculation
Connect a cell of EMF E, a plug key, a high resistance box R and the galvanometer (resistance G) all in series. The current is I = E/(R + G), so the deflection obeys θ = E/[k(R + G)]. Choose R values (a few thousand ohms) that give deflections spread between about 5 and 29 divisions, and record (R, θ) pairs.
For each pair compute k = E/[(R + G)θ] and take the mean. Even better, plot 1/θ against R: the points form a straight line with slope k/E, giving k graphically and exposing any rogue reading. G itself is usually supplied, or measured separately by the half-deflection method.
Precautions and the half-deflection idea
Never connect the galvanometer without the high resistance — full battery current would slam and possibly burn the coil. Start with the LARGEST R, close the key only briefly for each reading, and tap the case gently so the needle settles without sticking. Read at eye level to dodge parallax on the mirror scale.
The related half-deflection method finds G: with deflection θ at resistance R, add a shunt S across the galvanometer and adjust until deflection halves; then G = RS/(R − S) ≈ S when R is large. Examiners pair these two experiments constantly, so know both formulas.