Question 165: Current Electricity

Question

A galvanometer having coil resistance $$10 \Omega$$ shows a full scale deflection for a current of $$3 \mathrm{~mA}$$. For it to measure a current of $$8 \mathrm{~A}$$, the value of the shunt should be:

Accepted Answer

To determine the value of the shunt resistor required to convert the galvanometer into an ammeter capable of measuring a current of $$8 \mathrm{~A}$$, we need to use the concept of shunting where the additional resistor (shunt) is placed in parallel with the galvanometer.
The formula for calculating the value of the shunt resistor $ R_s $ is given by:
$$ R_s = \frac{R_g \cdot I_g}{I - I_g} $$
Where:
$ R_g $ = resistance of the galvanometer = $$10 \Omega$$
$ I_g $ = full-scale deflection current of the galvanometer = $$3 \mathrm{~mA}$$ = $$0.003 \mathrm{~A}$$
$ I $ = total current to be measured = $$8 \mathrm{~A}$$
Substituting these values into the formula:
$$ R_s = \frac{10 \Omega \cdot 0.003 \mathrm{~A}}{8 \mathrm{~A} - 0.003 \mathrm{~A}} $$
Perform the calculations:
$$ R_s = \frac{0.03 \Omega \cdot \mathrm{~A}}{7.997 \mathrm{~A}} $$
$$ R_s \approx 3.75 	imes 10^{-3} \Omega $$
Thus, the value of the shunt resistor should be:
Option A
: $$3.75 	imes 10^{-3} \Omega$$

Answer

$$3.75 	imes 10^{-3} \Omega$$

Answer

$$3 	imes 10^{-3} \Omega$$

Answer

$$4.85 	imes 10^{-3} \Omega$$

Answer

$$2.75 	imes 10^{-3} \Omega$$

Current Electricity

A galvanometer having coil resistance $10 \Omega shows a full scale deflection for a current of 3 \mathrm{~mA}. For it to measure a current of 8 \mathrm{~A}$, the value of the shunt should be:

Choose the correct answer: