A galvanometer of internal resistance 5 Ω has range 2 amps. In order to convert it into an ammeter of range 10 amps, how much shunt resistance is required?

A galvanometer of internal resistance 5 Ω has range 2 amps. In order to convert it into an ammeter of range 10 amps, how much shunt resistance is required? Correct Answer 1.25 Ω

Concept:

• A galvanometer can be converted into an ammeter by connecting a shunt resistance in parallel to it.
• The shunt resistance should have very low resistance. 
• So, the ammeter (the parallel combination of galvanometer and shunt resistance) will have low resistance.
• To convert a galvanometer into an ammeter of current rating ‘I’, a small resistance ‘S’ (shunt resistance) is connected in parallel across the galvanometer.

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V_g = (I - I_g) S = I_gR_g -- (1)

Where Vg is the voltage across the galvanometer, I is current in the circuit, Ig is the current is galvanometer, Rg is the resistance of galvanometer and S is the resistance of the shunt.

Calculation:

Given, resistance of galvanomter Rg = 5 Ω 

I_G = 2 A (Current through ammeter)

I = Current required I = 10 A. 

Using Equation (1)

(10 A - 2 A) S = 2 A × 5 Ω 

⇒ 8 A × S = 10 

⇒ S = 1.25 Ω

So the required resistance is 1.25 Ω.