Final answer:
To convert a 25Ω galvanometer that deflects fully at 10 mA to a voltmeter with a 100 V range, a series resistance of 9,975Ω is required, corresponding to option D.
Step-by-step explanation:
To convert a galvanometer into a voltmeter, a high resistance, labeled R, is placed in series with the galvanometer. The galvanometer has a resistance of 25Ω and gives a full-scale deflection at a current of 10 milliamperes (mA).
To extend the range of this galvanometer to measure up to 100 volts, we need to calculate the value of additional resistance required.
The voltage V across the entire series circuit (galvanometer plus series resistance R) can be given by Ohm's law V=I(R+rg), where I is the current, R is the additional series resistance, and rg is the internal resistance of the galvanometer.
Substituting I=10 mA, rg=25Ω, and V=100 volts into the equation, we get:
100 V = (10 mA)(R + 25Ω)
To find R, rearrange the equation:
R = (100 V / 10 mA) - 25Ω = 10,000Ω - 25Ω = 9,975Ω
Therefore, the resistance that must be added in series is 9,975Ω, which matches option D.