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Before a galvanometer can become an ammeter or a voltmeter, you need two numbers for it: its resistance G and its figure of merit k, the current for one division of deflection. The half-deflection method finds both with two resistance boxes and a battery. It is a short experiment, but the formula has an approximation hidden in it, and the viva often asks about it. This post derives the result, works a sample set of readings and shows when the shortcut fails.
Which syllabuses include it?
The CBSE Physics curriculum for 2026-27 lists "To determine resistance of a galvanometer by half-deflection method and to find its figure of merit" as experiment 4 in Section A of the Class 12 practicals. The JEE (Main) 2026 syllabus includes the same item under Experimental Skills. Check the documents for your year.
What is the principle?
Experiment 6 of the NCERT Class 12 physics lab manual sets it up like this. A battery of emf E, a high resistance box R and the galvanometer G are in series. A low resistance box S, with its own key, sits across the galvanometer.
Step 1, shunt open. The current is Ig = E/(R + G), and it gives a deflection θ. Since I = kθ, E/(R + G) = kθ.
Step 2, shunt closed. Keep R fixed and adjust S until the deflection is θ/2. The galvanometer and S are in parallel, so the galvanometer now carries I′g = ES / [R(G + S) + GS].
Setting Ig/I′g = 2 and simplifying, as the manual does:
R(G + S) + GS = 2S(R + G), so G = RS/(R − S)
The figure of merit follows from step 1: k = E / [(R + G)θ].
A worked set of readings
Sample numbers. E = 2.0 V. With R = 6400 Ω, the deflection is θ = 20 divisions. Closing the shunt key, the deflection drops to 10 divisions at S = 98 Ω.
G = RS/(R − S) = (6400 × 98)/(6400 − 98) = 627,200 / 6302 = 99.5 Ω
k = E / [(R + G)θ] = 2.0 / (6499.5 × 20) = 1.54 × 10⁻⁵ A per division, about 15 μA per division
The manual asks for five such sets with different R, then the mean of G and k.
Why must R be much larger than G?
The manual notes that for R much larger than S, G ≈ S. The idea is that closing the shunt barely changes the total current, so if the galvanometer's share halves, S must take the other half and so equal G.
How good is that? Take a galvanometer with G = 100 Ω.
With R = 6400 Ω, half deflection needs S = 98.5 Ω. Writing G ≈ S is 1.5 percent off.
With R = 1000 Ω, half deflection needs S = 90.9 Ω. G ≈ S is now 9 percent off.
So either use a large R, as the manual's precautions ask, or always use the full formula. The full formula is exact whatever R is, as long as the battery's internal resistance is negligible.
Can you use one-third deflection instead?
The manual's self-assessment asks this. Repeat the algebra with Ig/I′g = 3:
R(G + S) + GS = 3S(R + G), so RG = 2RS + 2GS, and G = 2RS/(R − 2S)
With R very large this tends to G = 2S, which makes sense: the galvanometer keeps a third of the current and the shunt takes two-thirds, so the shunt must have half the galvanometer's resistance. For G = 100 Ω and R = 6400 Ω, the shunt for one-third deflection is about 49.2 Ω.
What can go wrong?
The lab manual's precautions and sources of error:
Closing the key before setting a high R. A large current can burn the coil.
Odd deflections. Choose R so θ is an even number of divisions, so θ/2 is easy to read.
Changing emf. A weak cell gives a drifting deflection. Use a steady supply.
Loose or dirty plugs in the resistance boxes add unknown resistance.
Common mistakes and how to avoid them
Changing R after closing the shunt. R must stay fixed between the two steps.
Using S in place of G in k. Use the G you calculated.
Forgetting units for k. It is amperes per division, not amperes.
Wrong conversion afterwards. For an ammeter the shunt goes in parallel; for a voltmeter the high resistance goes in series. Our post on the moving coil galvanometer works through both.
A practice routine
Derive G = RS/(R − S) from the two current equations without looking.
Recompute the sample G and k, then redo G with R = 1000 Ω and S = 90.9 Ω.
Derive the one-third deflection formula and test it with the sample galvanometer.
For viva practice, explain in one sentence why R must be high. Our guide to CBSE practicals and viva has more questions like it.
If you can follow each line of the derivation but not why it works, Fermi's AI tutor can work out what you already know and build a plan for the session, so you sit down to a clear next step.
Before your next lab session, derive the formula once on paper and bring it with you.
