Question

A voltmeter of variable ranges 3 V, 15 V, 150 V is to be designed by connecting resistances R₁, R_2, R₃ in series with a galvanometer of resistance G = 20 Ω, as shown in Fig. The galvanometer gives full pass through its coil for 1 mA current i.e. "gives full pass through it's coil for 1 mA current". Then, the resistances R₁, R₂ and R₃ (in kilo ohms) should be, respectively:

Options

• 3, 12, 135

• 2.98, 12, 135

• 2.98, 14.98, 149.98

• None of these

Answer 1

2.98, 12, 135

Explanation:

R = `"V"/"I"_"g"-"R"_"g"`

 R₁ = `3/"I"_"g"-"R"_"g"`

= 2980 Ω = 2.98 kΩ

(R₁ + R₂) = `15/"I"_"g"-"R"_"g"`

= 14980 Ω

= 14.98 kΩ

(R₁ + R₂ + R₃) = `150/"I"_"g"-"R"_"g"` 

= 149980 Ω

= 149.98 kΩ

⇒ R₁ = 2.98 kΩ

R₂ = 14.98 - 2.98

= 12 kΩ

R₃ = 149.98 - 14.98

= 135 kΩ