A galvanometer of internal resistance 100 gives a full deflection for the residence necessary to the galvanometer to
To determine the resistance necessary for a galvanometer to give a full deflection, we need to consider the internal resistance of the galvanometer and its sensitivity.
A galvanometer is an instrument used to detect small electric currents. It consists of a coil of wire suspended between the poles of a permanent magnet. When an electric current passes through the coil, it generates a magnetic field that interacts with the magnetic field of the permanent magnet, causing the coil to rotate.
The sensitivity of a galvanometer is a measure of how easily the coil is deflected by a given amount of current. It is usually given in terms of the deflection per unit current. For example, if the sensitivity is 1 division per microampere (µA), then a current of 1 µA will cause the coil to deflect by 1 division.
The internal resistance of the galvanometer is the resistance within the galvanometer itself, which affects the amount of current that can pass through it. A higher internal resistance will limit the current flow, resulting in a smaller deflection.
In this case, the galvanometer has an internal resistance of 100 ohms and gives a full deflection. To find the resistance necessary for this deflection, we can use Ohm's Law. Ohm's Law states that the current flowing through a resistor is equal to the voltage across the resistor divided by the resistance:
I = V / R
In this case, the current is the maximum current that gives a full deflection, and the voltage is the maximum voltage across the galvanometer.
To find the maximum voltage across the galvanometer, we can use the formula for the maximum voltage in a circuit:
V = I * (R + r)
Where V is the maximum voltage, I is the maximum current, R is the external resistance, and r is the internal resistance of the galvanometer.
Since the internal resistance of the galvanometer is given as 100 ohms, we substitute that value into the equation:
V = I * (R + 100)
Since the galvanometer gives a full deflection, the maximum current is the maximum current that can pass through the galvanometer, given by:
I = V / r
Substituting V / r for I in the previous equation:
V = (V / r) * (R + 100)
Now, we can solve this equation for R to find the necessary resistance for a full deflection. Rearranging the equation, we get:
V = V * (R + 100) / r
Multiplying both sides by r:
Vr = V * (R + 100)
Dividing both sides by V:
r = (R + 100)
Substituting the given value of r as 100 ohms, we get:
100 = R + 100
Subtracting 100 from both sides:
0 = R
Therefore, the necessary external resistance for the galvanometer to give a full deflection is 0 ohms.