A galvanometer of resistance 50 ohm which gives a full deflection for 1mA is to be adapted to measure currents up to 5A. Calculate the resistance of the resistor required
5A = 5,000mA.
Ig = 1mA. = Current through the galvanometer.
Ir = 4,999mA = Current through the resistor.
R = (1mA/4,999mA) * 50 Ohms = 0.01 Ohms in parallel with the galvanometer.
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To adapt the galvanometer to measure currents up to 5A, we need to add a shunt resistor in parallel to the galvanometer. The purpose of the shunt resistor is to divert most of the current away from the galvanometer, allowing only a smaller fraction of the total current to pass through it.
To calculate the resistance of the shunt resistor, we can use the formula:
I_total = I_galvanometer + I_shunt,
where I_total is the total current, I_galvanometer is the current passing through the galvanometer, and I_shunt is the current passing through the shunt resistor.
In this case, we want the full-scale deflection of the galvanometer to occur at 5A, so I_galvanometer = 1mA = 0.001A.
Therefore, I_total = 5A and I_shunt = I_total - I_galvanometer = 5A - 0.001A = 4.999A.
Now we can use Ohm's law to calculate the resistance of the shunt resistor:
R_shunt = V_shunt / I_shunt,
where V_shunt is the voltage across the shunt resistor.
Since the shunt resistor is connected in parallel to the galvanometer, they share the same voltage:
V_shunt = V_galvanometer = I_galvanometer * R_galvanometer.
Substituting the known values:
V_shunt = 0.001A * 50Ω = 0.05V.
Now we can calculate the resistance of the shunt resistor:
R_shunt = 0.05V / 4.999A = 0.01Ω.
Therefore, the resistance of the resistor required is 0.01Ω.