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 :

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Current Electricity

For designing a voltmeter of range 50 V and an ammeter of range 10 mA using a galvanometer which has a coil of resistance

54Ω

showing a full scale deflection for 1 mA as in figure.

(A) for voltmeter

R \approx 50 k Ω

(B) for ammeter

r \approx 0.2Ω

r \approx 6Ω

(D) for voltmeter

R \approx 5 k Ω

(E) for voltmeter

R \approx 500Ω

Choose the correct answer from the options given below :

Answer: (C)

For the voltmeter a resistance

R

is placed in series so that full-scale current flows at

50 V

R = \frac{V}{I _{g}} - G = \frac{50}{1 0 ^{- 3}} - 54 \approx 50 k Ω

. For the ammeter a shunt

r

carries the surplus current:

r = \frac{I _{g} G}{I - I _{g}} = \frac{1 0 ^{- 3} \times 54}{( 10 - 1 ) \times 1 0 ^{- 3}} = 6 Ω

. Thus the voltmeter needs about

50 k Ω

in series and the ammeter about

6 Ω

as a shunt.

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Single correct option