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SMA Physics • Physics Lab Class XII • Exp 14

🧲 Galvanometer Resistance & Figure of Merit

📖 Manual
⚡ Interactive Half-Deflection Circuit Schematic
💡
Step 1: Insert Key $K_1$ (keep $K_2$ open). Adjust series resistance $R$ until the galvanometer indicates an even deflection $\theta$ (e.g. 26 to 30 divisions).
Key $K_1$: OPEN
Key $K_2$ (Shunt): OPEN
Galv Deflection $\theta$: 0.0 div
Galv Current $I_g$: 0.0 μA
🎛️ Laboratory Circuit Controls $E = 2.00\text{ V}$
Plug Keys ($K_1$ & $K_2$) Click to Insert/Remove
High Resistance Box ($R$) 4500 Ω
Range: 1000 Ω to 10,000 Ω Series Resistor
Shunt Resistance Box ($S$) 75 Ω
Range: 5 Ω to 250 Ω Parallel Shunt
📐 Computed Physical Constants
Galvanometer Resistance $G$
-- Ω
Figure of Merit $k$
-- A/div
Current Sensitivity $S_i$
-- div/μA
Full-Scale Deflection $I_g$
-- μA

Table of Observations: Half-Deflection Method

EMF of Accumulator / DC Supply $E = 2.00\text{ V}$, Scale Divisions $n = 30$

S.No. EMF $E$ (V) High Res $R$ (Ω) Initial Defl $\theta$ (div) Shunt $S$ (Ω) Half Defl $\theta/2$ (div) Galv Res $G = \frac{R \cdot S}{R - S}$ (Ω) Figure of Merit $k = \frac{E}{(R+G)\theta}$ (A/div)
📊 Experimental Mean Results
Mean Galvanometer Resistance ($G$)
-- Ω
Mean Figure of Merit ($k$)
-- A/div

Graph Analysis: $1/\theta$ vs $R$

Equation: $\frac{1}{\theta} = \frac{k}{E} R + \frac{k G}{E}$. Slope $= \frac{k}{E}$, Intercept on negative $R$-axis $= -G$.

ℹ️
Record at least 3 distinct pairs of $(R, \theta)$ with $K_2$ open to draw the linear regression curve. The negative intercept on the horizontal resistance axis gives the internal resistance $G$ of the galvanometer!

🎯 Aim of the Practical

To determine the resistance of a moving coil galvanometer by half-deflection method and to find its figure of merit ($k$).

📐 Governing Mathematical Theory

When high resistance $R$ is connected in series with the galvanometer of resistance $G$ across an EMF source $E$, with key $K_1$ closed and $K_2$ open:

$$I = \frac{E}{R + G} = k \cdot \theta \implies \theta = \frac{E}{k(R + G)}$$

When shunt resistance $S$ is connected in parallel with the galvanometer by closing key $K_2$, the effective parallel resistance becomes $G_p = \frac{G S}{G + S}$. The total current is $I' = \frac{E}{R + \frac{GS}{G+S}}$, and the current dividing into the galvanometer branch is:

$$I_g = I' \cdot \frac{S}{G + S} = \frac{E \cdot S}{R(G + S) + GS} = k \cdot \theta'$$

By adjusting the shunt resistance $S$ such that $\theta' = \frac{\theta}{2}$, we obtain:

$$G = \frac{R \cdot S}{R - S}$$

Since $R \gg S$, $R - S \approx R$, hence $G \approx S$. The figure of merit $k$ (current required to produce unit division deflection) is calculated as:

$$k = \frac{E}{(R + G)\theta} \quad \text{(A/div)}$$

❓ Interactive Viva Voce Preparation