A galvanometer has an internal resistance of 19.0\text{ }\Omega and produces a full-scale … — JAMB UTME

A galvanometer has an internal resistance of $19.0\text{ }\Omega$ and produces a full-scale deflection for a current of $50\text{ mA}$ . What value of shunt resistance, in ohms ( $\Omega$ ), must be connected in parallel with the galvanometer to convert it into an ammeter capable of measuring currents up to $1.0\text{ A}$ ?

Answer: 1 Ω

Answer

The required shunt resistance is

1.0\text{ }\Omega

To convert a sensitive galvanometer into an ammeter, a low-resistance resistor called a shunt (

R_s

) is connected in parallel with the galvanometer. This provides an alternative path for the bulk of the total current. Since the potential difference across parallel branches is equal,

I_s R_s = I_g R_g

. Substituting

I_g = 0.05\text{ A}

R_g = 19.0\text{ }\Omega

, and

I_s = 1.0\text{ A} - 0.05\text{ A} = 0.95\text{ A}

yields

R_s = \frac{0.05 \times 19.0}{0.95} = 1.0\text{ }\Omega

Step-by-Step Solution

Convert the galvanometer full-scale deflection current

I_g

to amperes.

I_g = 50\text{ mA} = 0.05\text{ A}

Standard SI units must be used for electrical calculations.

Calculate the current

I_s

that must bypass the galvanometer through the shunt resistor.

I_s = I - I_g = 1.0\text{ A} - 0.05\text{ A} = 0.95\text{ A}

By Kirchhoff's current law, the total maximum current splits into galvanometer current and shunt current.

Calculate the required shunt resistance

R_s

using the parallel voltage relation.

R_s = \frac{I_g R_g}{I_s} = \frac{0.05\text{ A} \times 19.0\text{ }\Omega}{0.95\text{ A}} = 1.0\text{ }\Omega

Because the galvanometer and shunt resistor are connected in parallel, they share the exact same potential difference.

Key Concept

Galvanometer Conversion to Ammeter using a Shunt Resistor

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