Question

A galvanometer has a resistance of 30Ω and its full scale deflection current is 20 microamperes (\(\mu A\)). What resistance should be added to it to have a range of 0-10 volts?

Hint:

To extend a galvanometer's range to measure higher voltages, a large-value resistor is added in series to limit the current flowing through the galvanometer.

Answer 1

To convert a galvanometer into a voltmeter, a resistance needs to be connected in series with the galvanometer. The total resistance \( R \) is given by: \[ R = \frac{V}{I} \] where \( V = 10 \, {V} \) is the desired voltmeter range, and \( I = 20 \, \mu A = 20 \times 10^{-6} \, {A} \) is the full-scale deflection current. Substituting these values: \[ R = \frac{10}{20 \times 10^{-6}} = 500,000 \, \Omega. \] Given that the galvanometer has an internal resistance of \( 30 \, \Omega \), the resistance to be added is: \[ R_{{added}} = 500,000 - 30 = 499,970 \, \Omega. \]