Combination Of Resistors Series And Parallel

Let the resistance of the smaller resistor be and that of the larger resistor be .
The balance point in a meter bridge is given by the formula: where is the balance point and are the resistances of the two resistors.
Initially, the balance point is 20 cm, so: This simplifies to:
When a 15 ohm resistor is connected in series with , the new balance point shifts to 40 cm. The total resistance of the smaller side becomes . The new equation is: This simplifies to:
Now, solve equations (1) and (2) together: From equation (1), . Substitute this into equation (2): Simplifying: Cross-multiply: