What is the formula for voltmeter in galvanometer?
2 Answers
To convert a galvanometer into a voltmeter, you need to use a shunt resistor. The formula for the total voltage (\(V\)) across the galvanometer when connected to a voltage source can be expressed in terms of the galvanometer's full-scale deflection current (\(I_g\)) and the resistance of the galvanometer (\(R_g\)).
The relationship is given by:
\[
V = I_g \cdot R_g
\]
When a galvanometer is used as a voltmeter, it is often connected in series with a resistor \(R_s\) (the shunt resistor) to allow it to measure higher voltages. The total voltage can also be expressed as:
\[
V = I \cdot R_g + I_s \cdot R_s
\]
Where:
- \(I\) is the total current through the circuit,
- \(I_s\) is the current through the shunt resistor, and it can be calculated as:
\[
I_s = I - I_g
\]
From these relationships, you can find the necessary shunt resistance \(R_s\) for a given voltage range using the formula:
\[
R_s = \frac{R_g \cdot I_g}{V - I_g \cdot R_g}
\]
This way, you can set up a galvanometer to measure voltages without exceeding its full-scale deflection.
The relationship is given by:
\[
V = I_g \cdot R_g
\]
When a galvanometer is used as a voltmeter, it is often connected in series with a resistor \(R_s\) (the shunt resistor) to allow it to measure higher voltages. The total voltage can also be expressed as:
\[
V = I \cdot R_g + I_s \cdot R_s
\]
Where:
- \(I\) is the total current through the circuit,
- \(I_s\) is the current through the shunt resistor, and it can be calculated as:
\[
I_s = I - I_g
\]
From these relationships, you can find the necessary shunt resistance \(R_s\) for a given voltage range using the formula:
\[
R_s = \frac{R_g \cdot I_g}{V - I_g \cdot R_g}
\]
This way, you can set up a galvanometer to measure voltages without exceeding its full-scale deflection.