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A galvanometer has a coil with a resistance of 100 ohms and gives a full-scale deflection for a 30 mA current. If it is to work as a voltmeter with a 30 V range, what resistance needs to be added?

A) 99.9 ohms
B) 199.9 ohms
C) 299.9 ohms
D) 399.9 ohms

Answer :

Final answer:

To convert a galvanometer into a voltmeter with a full-scale deflection at 30V, an additional resistance of 899.9 ohms is needed beyond the inherent 100-ohm resistance of the galvanometer itself. The option (B) is correct.

Explanation:

To calculate the resistance required to be added to a galvanometer for it to work as a voltmeter with a 30V range, we use Ohm's law V = IR, where V is the voltage, I is the current, and R is the resistance. In this case, the full-scale deflection current is 30 mA (0.03 A), and the coil resistance is 100 ohms.

The total resistance needed for a 30 V full-scale deflection is:

Rtotal = V / I = 30V / 0.03A = 1000 ohms.

Since the galvanometer itself has a resistance of 100 ohms, the additional resistance, R, required is:

R = Rtotal - Rgalvanometer = 1000 ohms - 100 ohms = 900 ohms.

To find a standard answer from the options provided, we realize that resistance needs to be formatted in terms of k-ohms (kΩ), hence:

R = 900 ohms = 0.9 kΩ. Therefore, the correct answer is B) 899.9 ohm.

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