The resistance of an ammeter is 13 Ω and its scale is graduated for a current up to 100 A. After an additional

Question

The resistance of an ammeter is 13 Ω and its scale is graduated for a current up to 100 A. After an additional shunt has been connected to this ammeter, it becomes possible to measure currents up to 750 A by this ammeter. The value of shunt resistance is:

Accepted Answer

1. **Concept:** An ammeter (or galvanometer) with resistance $R_G$ and full-scale deflection current $I_g$ can have its range extended to measure a larger current $I$ by connecting a low resistance shunt ($S$) in parallel with it .
2. **Formula:** The potential drop across the galvanometer and the shunt is the same in a parallel combination. Therefore:
   $$I_g R_G = (I - I_g) S$$
   Rearranging for the shunt resistance $S$:
   $$S = \frac{I_g R_G}{I - I_g}$$
3. **Given Values:**
   - Resistance of the initial meter ($R_G$) = 13 Ω
   - Initial full-scale current ($I_g$) = 100 A
   - New full-scale current ($I$) = 750 A
4. **Calculation:**
   $$S = \frac{100 	imes 13}{750 - 100}$$
   $$S = \frac{1300}{650}$$
   $$S = 2 \, \Omega$$

Step-by-Step Solution

Practice All PHYSICS Questions