A galvanometer needle deflects full scale for 53.0A current. What current will
give full-scale deflection if the magnetic field weakens to 0.860 of its original
value?
To find the current that will give a full-scale deflection when the magnetic field weakens to 0.860 of its original value, we can use the concept of proportionality.
Let's consider the proportionality between the current and the magnetic field strength. We can write this proportionality as:
Current ∝ Magnetic Field Strength
Since we know that the galvanometer needle deflects at full-scale for a current of 53.0A, we can assume that this current corresponds to the original magnetic field strength.
Now, if the magnetic field weakens to 0.860 of its original value, we can express this as:
New Magnetic Field Strength = 0.860 * Original Magnetic Field Strength
To find the current that will give full-scale deflection with this weakened magnetic field strength, we can apply the same proportionality relation:
New Current ∝ New Magnetic Field Strength
We can rearrange the above equation to find the new current:
New Current = (New Magnetic Field Strength / Original Magnetic Field Strength) * Original Current
Substituting the given values:
Original Current = 53.0A
Original Magnetic Field Strength = 1 (since it is the original value)
New Magnetic Field Strength = 0.860 * 1 = 0.860
Calculating the new current:
New Current = (0.860 / 1) * 53.0A
New Current = 45.58A
Therefore, the current that will give a full-scale deflection when the magnetic field weakens to 0.860 of its original value is approximately 45.58A.