A galvanometer of resistance $76 \Omega$ gives full scale deflection when only 5% of total current passes through it. The value of shunt is:

$4 \Omega$

The correct answer is Option (2) → $4 \Omega$

The voltage across the galvanometer is the same as the voltage across the shunt resistor.

$V_g=I_gR_g$ [Ohm's law]

and for shunt Resistor,

$V_s=I_sR_s$

and $I_s=0.95I$ because 95% of current pass through shunt resistance.

$V_g=I_s$ [given]

$I_gR_g=I_sR_s$

$0.05I.R_g=0.95I.R_s$

$R_s=\frac{0.05×76}{0.95}=\frac{3.8}{0.95}≃4Ω$