Converting a Galvanometer to a DC Voltmeter

A galvanometer is a sensitive instrument that can detect small electric currents. To convert it into a DC voltmeter, a high resistance, known as a multiplier resistance, is connected in series with the galvanometer. This series resistance increases the overall resistance of the instrument and limits the current flowing through the galvanometer coil, allowing it to measure larger voltages.

The full-scale deflection current (\(I_g\)) of the galvanometer represents the maximum current the galvanometer can safely handle. When used as a voltmeter, this current will flow through the galvanometer and the series resistance when the maximum voltage (\(V\)) of the desired range is applied across the combination.

The total resistance of the voltmeter (\(R_v\)) is the sum of the galvanometer's internal resistance (\(R_g\)) and the series multiplier resistance (\(R_s\)):

\(R_v = R_g + R_s\)

According to Ohm's Law, the voltage across the voltmeter at full-scale deflection is given by:

\(V = I_g \times R_v\)

Substituting the expression for \(R_v\):

\(V = I_g (R_g + R_s)\)

We want to find the value of the multiplier resistance, \(R_s\). We can rearrange the formula to solve for \(R_s\):

\(\frac{V}{I_g} = R_g + R_s\)

\(R_s = \frac{V}{I_g} - R_g\)

Calculating the Multiplier Resistance

We are given the following values:

• Internal resistance of the galvanometer, \(R_g = 100 \, \Omega\)
• Full-scale current of the galvanometer, \(I_g = 1 \, \text{mA} = 1 \times 10^{-3} \, \text{A}\)
• Desired full-scale voltage range, \(V = 500 \, \text{V}\)

Now, let's substitute these values into the formula for \(R_s\):

\(R_s = \frac{500 \, \text{V}}{1 \times 10^{-3} \, \text{A}} - 100 \, \Omega\)

\(R_s = 500 \times 10^3 \, \Omega - 100 \, \Omega\)

\(R_s = 500000 \, \Omega - 100 \, \Omega\)

\(R_s = 499900 \, \Omega\)

Thus, a series resistance of \(499900 \, \Omega\) is required to convert the given galvanometer into a DC voltmeter with a range of 0 V - 500 V.