A galvanometer coil has a resistance of 14 Ω and the metre shows full scale deflection for a current of 4 mA. How will you convert the metre into a voltmeter of range 0 to 16 V?

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  1. A resistor of resistance 5988 Ω is to be connected in series with the galvanometer
  2. A resistor of resistance 5988 Ω is to be connected in parallel with the galvanometer
  3. A resistor of resistance 3986 Ω is to be connected in series with the galvanometer
  4. A resistor of resistance 3986 Ω is to be connected in parallel with the galvanometer

Answer (Detailed Solution Below)

Option 3 : A resistor of resistance 3986 Ω is to be connected in series with the galvanometer
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Detailed Solution

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Given:

Galvanometer coil resistance (Rg)= 14 Ω 

Full scale deflection current (ig= 4 mA or (0.004 A)

Voltmeter range (V) = 16 V 

Concept:

For converting a galvanometer into a voltmeter, we connect a high resistance in series with the galvanometer coil.

The voltmeter is then connected in parallel across the terminals for which potential difference is to be measured.

Formula:

ig(R + Rg) = V

⇒ R = V/ig - Rg

Calculation:

R = (16/0.004 - 14)

⇒ R = 4000 - 14

= 3986 Ω

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