Derivation of G=RS÷(R-S) where G is resistance of galvanometer
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Derivation of G = RS ÷ (R - S):
The resistance of the galvanometer is used with half deflection method.
The below given is the simple circuit to find the resistance of the galvanometer.
From the diagram:
- and are keys
- G is the resistance of the galvanometer
- E is EMF of the cell
- I is current
- H.R.B is high resistance box
- L.R.B is low resistance box
Condition 1:
is closed and is opened
Current flowing through galvanometer is
Where,
R is resistance through H.R.B
Current flowing through moving coil galvanometer is
Where,
Condition 2:
is opened and is closed
Current flowing through galvanometer is
Now, the deflection of the galvanometer is maintained half.
From equation (2) and (4),
Thus,
By parallel combination of resistors
On substituting equation (5) and (6) in above equation, we get,
On substituting equation (1) and (3) in above equation, we get,
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