A galvanometer having a coil resistance of 60 $\Omega$ shows full scale deflection when a current of 1.0 A pas

Question

A galvanometer having a coil resistance of 60 $\Omega$ shows full scale deflection when a current of 1.0 A passes through it. It can be converted into an ammeter to read currents upto 5.0 A by

Accepted Answer

1. **Concept:** To convert a galvanometer into an ammeter (which measures larger currents), a low resistance called a **shunt** ($S$) must be connected in **parallel** with the galvanometer coil. This allows the excess current to bypass the sensitive coil .
2. **Formula:** Since the galvanometer and shunt are in parallel, the potential difference across them is the same:
   $$I_g G = (I - I_g) S$$
   Where:
   - $I_g$ is the full-scale deflection current ($1.0 	ext{ A}$).
   - $G$ is the galvanometer resistance ($60 \Omega$).
   - $I$ is the total current to be measured ($5.0 	ext{ A}$).
   - $S$ is the required shunt resistance.
3. **Calculation:** Rearranging the formula to solve for $S$:
   $$S = \frac{I_g G}{I - I_g}$$
   $$S = \frac{1.0 	imes 60}{5.0 - 1.0}$$
   $$S = \frac{60}{4} = 15 \Omega$$
4. **Conclusion:** A resistance of $15 \Omega$ must be connected in parallel .

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