Question 12

For designing a voltmeter of range 50 V and an ammeter of range 10 mA using a galvanometer which has a coil of resistance 54 $$\Omega$$ showing a full scale deflection for 1 mA as in figure.

(A) for voltmeter $$R \approx 50$$ k$$\Omega$$
(B) for ammeter $$r \approx 0.2 \ \Omega$$
(C) for ammeter $$r \approx 6 \ \Omega$$
(D) for voltmeter $$R \approx 5$$ k$$\Omega$$
(E) for voltmeter $$R \approx 500 \ \Omega$$
Choose the correct answer from the options given below:

Galvanometer: $$G = 54 \ \Omega$$, $$I_g = 1$$ mA.

For voltmeter (range 50 V):

$$R = \frac{V}{I_g} - G = \frac{50}{0.001} - 54 = 50000 - 54 = 49946 \approx 50 \text{ k}\Omega$$

Statement (A) is correct: $$R \approx 50$$ k$$\Omega$$.

For ammeter (range 10 mA):

$$r = \frac{G \cdot I_g}{I - I_g} = \frac{54 \times 0.001}{0.01 - 0.001} = \frac{0.054}{0.009} = 6 \ \Omega$$

Statement (C) is correct: $$r \approx 6 \ \Omega$$.

The correct answer is option 1: (A) and (C).

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