In a Wheatstone bridge, with applied voltage of 40 volts and specific resistances, how is the resistance of the third resistor calculated to balance the bridge?

In a Wheatstone bridge, the principle behind balancing the bridge involves the ratios of the known resistances. When you have a setup where four resistors are configured into a diamond shape, the bridge is balanced when the voltage across the middle points is zero.

To achieve this balance, the resistance of the third resistor can be calculated using the known values of the other resistors. The relationship governing the bridge at balance is given by the equation:

R1 / R2 = R3 / R4

where R1 and R2 are the known resistances, and R3 is the resistance you want to determine, while R4 is the other known resistance. By rearranging this formula, you can express R3 in terms of the other values, allowing you to calculate the necessary resistance to maintain the balance.

This method allows for precise calculations without needing to alter the physical setup or rely on measurement techniques that could introduce errors. It highlights the importance of understanding circuit theory and the relationships between components in achieving electrical balance in the circuit.