How do I convert a galvanometer into an ammeter or a voltmeter?

At full scale the coil has U_g = IgRg. For an ammeter of range I, a parallel shunt must carry I − Ig: R_sh = IgRg / (I − Ig) = Rg / (n − 1) with n = I/Ig. For a voltmeter of range U, add a series multiplier R_m = U/Ig − Rg = (n − 1)Rg with n = U/U_g. With Ig = 1 mA and Rg = 100 Ω, a 0.6 A ammeter needs about 0.167 Ω and a 3 V voltmeter needs 2900 Ω.

When should the ammeter go inside or outside the voltmeter?

Ammeter inside: the voltmeter also reads the ammeter’s drop, so R_m = R + R_A, too high. Ammeter outside: the ammeter also carries the voltmeter current, so R_m = R·R_V/(R + R_V), too low. Compare R with √(R_A·R_V): use the internal connection for larger R and the external connection for smaller R.

Why is an ohmmeter scale uneven, and what is the mid-scale resistance?

After zeroing, the meter’s internal resistance is R_in = E/Ig. With Rx connected, I/Ig = R_in/(R_in + Rx), which is not proportional to Rx, so the scale runs from 0 on the right to ∞ on the left and crowds to the left. When Rx = R_in the needle sits exactly in the middle, so the mid-scale value equals the internal resistance. Readings are most accurate near the middle.

What errors do the two EMF circuits give?

With the voltmeter straight across the cell (the usual textbook circuit), the voltmeter draws current and the equivalent source is the cell in parallel with R_V: E_m = E·R_V/(R_V + r) and r_m = r·R_V/(R_V + r), both slightly low but tiny because R_V ≫ r. With the ammeter in series with the cell, E_m = E exactly but r_m = r + R_A, which for a dry cell can exceed r itself.

Why does the half-deflection method read the coil resistance low?

You set full scale with S₂ open, then close S₂ and adjust the decade box R₂ to half scale and take R₂ as Rg. Closing S₂ lowers the circuit resistance, so the total current rises a little above Ig and R₂ carries more than Ig/2, hence R₂ < Rg. Exactly R₂ = A·Rg/(A + Rg) with A = R₁ + r, an error of about −Rg/A. A larger supply EMF needs a larger R₁ and gives a smaller error. The voltmeter half-deflection method reads high instead.

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🎛️Meter Conversion & Electrical Measurements - shunt, multiplier, ohmmeter, EMF

The meter-related parts of school electrical practicals in one place. Enter a galvanometer’s Ig and Rg to get the shunt for an ammeter or the series multiplier for a voltmeter, watch the needle swing on a dual scale, and see how a resistor error biases the reading. The ohmmeter page draws the non-linear scale (0 on the right, ∞ on the left) and explains the mid-scale resistance and why an aged cell reads high. The voltmeter–ammeter page compares internal and external connections against √(R_A·R_V). The EMF page fits E and r from noisy simulated U–I data for both circuits, and the last page covers the Wheatstone bridge and the half-deflection method.

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How to use Meter Conversion & Electrical Measurements

1On Meter conversion enter Ig, Rg and the target range to get the resistor
2On Ohmmeter change E and Rx, watch the non-linear scale and try an aged cell
3On the voltmeter–ammeter and EMF pages switch the connection and compare with true values
4On Bridge & half-deflection balance the bridge and see how the half-deflection error depends on E

FAQ

How do I convert a galvanometer into an ammeter or a voltmeter?: At full scale the coil has U_g = IgRg. For an ammeter of range I, a parallel shunt must carry I − Ig: R_sh = IgRg / (I − Ig) = Rg / (n − 1) with n = I/Ig. For a voltmeter of range U, add a series multiplier R_m = U/Ig − Rg = (n − 1)Rg with n = U/U_g. With Ig = 1 mA and Rg = 100 Ω, a 0.6 A ammeter needs about 0.167 Ω and a 3 V voltmeter needs 2900 Ω.
When should the ammeter go inside or outside the voltmeter?: Ammeter inside: the voltmeter also reads the ammeter’s drop, so R_m = R + R_A, too high. Ammeter outside: the ammeter also carries the voltmeter current, so R_m = R·R_V/(R + R_V), too low. Compare R with √(R_A·R_V): use the internal connection for larger R and the external connection for smaller R.
Why is an ohmmeter scale uneven, and what is the mid-scale resistance?: After zeroing, the meter’s internal resistance is R_in = E/Ig. With Rx connected, I/Ig = R_in/(R_in + Rx), which is not proportional to Rx, so the scale runs from 0 on the right to ∞ on the left and crowds to the left. When Rx = R_in the needle sits exactly in the middle, so the mid-scale value equals the internal resistance. Readings are most accurate near the middle.
What errors do the two EMF circuits give?: With the voltmeter straight across the cell (the usual textbook circuit), the voltmeter draws current and the equivalent source is the cell in parallel with R_V: E_m = E·R_V/(R_V + r) and r_m = r·R_V/(R_V + r), both slightly low but tiny because R_V ≫ r. With the ammeter in series with the cell, E_m = E exactly but r_m = r + R_A, which for a dry cell can exceed r itself.
Why does the half-deflection method read the coil resistance low?: You set full scale with S₂ open, then close S₂ and adjust the decade box R₂ to half scale and take R₂ as Rg. Closing S₂ lowers the circuit resistance, so the total current rises a little above Ig and R₂ carries more than Ig/2, hence R₂ < Rg. Exactly R₂ = A·Rg/(A + Rg) with A = R₁ + r, an error of about −Rg/A. A larger supply EMF needs a larger R₁ and gives a smaller error. The voltmeter half-deflection method reads high instead.

Features

Ammeter and voltmeter conversion: shunt, multiplier, range factor, new meter resistance
Damped swinging needle on a dual scale, with the reading error from an off-value resistor
Ohmmeter non-linear scale, mid-scale resistance and aged-cell error
Internal vs external connection: error formulas, critical resistance and error curves
EMF and internal resistance: simulated data, U–I fit and the theoretical bias of both circuits
Wheatstone bridge galvanometer current, current and voltage half-deflection errors

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