Final answer:
To convert a galvanometer into a voltmeter with an increased range, calculate the series resistance needed using the formula R = G/(n-1), where G is the galvanometer's resistance, and n is the range multiplier.
Step-by-step explanation:
To convert a galvanometer into a voltmeter with a higher range, a high-value resistor must be connected in series with it. If the galvanometer has a resistance of G ohms and is initially set to have a full-scale deflection at V volts, and you wish to upgrade it to have a full-scale deflection at nC volts, where n is the multiplier for the new range, you would need to calculate the resistance R to add in series.
The total resistance required for the voltmeter to achieve the full-scale deflection at nC volts is Rtot = nC/G. To find the value of the series resistance R to add, you subtract the internal resistance G of the galvanometer from Rtot, yielding R = Rtot - G. Substituting Rtot gives R = (nC/G) - G, which simplifies to R = G(n-1)/n. Hence, the resistance used in series to convert it into a voltmeter of range nC volts is R = G/(n-1).