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SMA Physics ā€¢ Physics Lab Class XII ā€¢ Exp 15

šŸ“Ÿ Conversion of Galvanometer into Voltmeter

šŸ“– Manual
āš” Dual Instrument Visual Comparison & Potential Divider
šŸ’”
Experiment Protocol: Slide the potential divider jockey across the rheostat to vary voltage $V$. Compare the reading on the Standard Master Voltmeter ($V_{\text{std}}$) with the Converted Galvanometer ($V_{\text{calc}} = \theta \times \text{LC}$).
Desired Range: 0 to 3.0 V
Multiplier Resistor $R$: 4925 Ī©
Standard Voltmeter $V_1$: 0.00 V
Galv Deflection $\theta$: 0.0 div
šŸŽ›ļø Multiplier Design & Rheostat Controls $G = 75\ \Omega,\ k = 20\ \mu\text{A/div}$
Select Target Voltmeter Range ($V_{\text{max}}$) 3.0 V
0 ā€“ 3.0 V
0 ā€“ 5.0 V
0 ā€“ 10.0 V
Potential Divider Rheostat Slider (Jockey) 0 %
Position across Rheostat ($0 - 100\%$) 0.00 V Applied
Battery Key ($K$) 4.0V Supply
šŸ“ Dual Reading & Error Analysis
Standard Voltmeter ($V_1$)
0.00 V
Converted Voltmeter ($V_2$)
0.00 V
Least Count (LC = $V/n$)
0.100 V/div
Discrepancy Error ($\Delta V = V_2 - V_1$)
0.00 V

Verification Table: Galvanometer Converted into Voltmeter

Desired Range: $0 - V$, Scale Divisions $n = 30$, Series Multiplier $R = \frac{V}{I_g} - G$

S.No. Standard Voltmeter $V_1$ (V) Galv Deflection $\theta$ (div) Converted Voltmeter $V_2 = \theta \times \text{LC}$ (V) Difference / Error $\Delta V = V_2 - V_1$ (V) Remarks / Accuracy
šŸ“Š Calibration Summary
Maximum Absolute Error ($|\Delta V|_{\text{max}}$)
-- V
Mean Calibration Error
-- V

Calibration Error Curve: $\Delta V$ vs $V_{\text{std}}$

Plotting discrepancy $\Delta V = (V_2 - V_1)$ against standard voltmeter reading $V_1$.

ā„¹ļø
The calibration error graph demonstrates instrument precision across the operating voltage range. In a well-constructed multiplier circuit, deviations are minor and lie within permissible laboratory limits ($\pm 0.02\text{ V}$).

šŸŽÆ Aim of the Experiment

To convert the given moving coil galvanometer (of known resistance $G$ and figure of merit $k$) into a voltmeter of desired range (say $0 - V$ volts) and to verify the same with a standard voltmeter.

šŸ“ Design Formulae & Mathematical Principles

A galvanometer is a very sensitive current-detecting instrument. To convert it into a voltmeter measuring potential difference up to $V$ volts, a large multiplier resistance $R$ must be connected in series with the galvanometer coil.

$$I_g = n \cdot k$$

Where $n$ is total scale divisions ($n = 30$) and $k$ is the figure of merit ($2.0 \times 10^{-5}\text{ A/div}$), yielding full-scale deflection current $I_g = 600\ \mu\text{A} = 0.0006\text{ A}$.

By Ohm's Law, when maximum voltage $V$ is applied across the combination:

$$V = I_g (R + G) \implies R = \frac{V}{I_g} - G$$

For example, to design a $0 - 3.0\text{ V}$ voltmeter using $G = 75\ \Omega$:

$$R = \frac{3.0}{0.0006} - 75 = 5000 - 75 = 4925\ \Omega$$

The least count of the converted voltmeter is:

$$\text{Least Count (LC)} = \frac{V}{n} = \frac{3.0}{30} = 0.1\text{ V/div}$$

ā“ Interactive Viva Voce Preparation