Explain the principle of Wheatstone bridge and derive the formula for balance condition

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A Wheatstone bridge is a type of circuit used to measure an unknown electrical resistance. The circuit consists of four resistors arranged in a diamond pattern, with a voltmeter connected across the middle of the diamond. When an unknown resistor is placed in one of the corners of the diamond, the other three resistors can be adjusted until the voltmeter reads zero. This indicates that the circuit is in balance and that the unknown resistance can be calculated using Ohm’s law.

The formula for the balance condition of a Wheatstone bridge is given by:

V = IR

where V is the voltage across the unknown resistor, I is the current through the circuit, and R is the unknown resistance.

To calculate the unknown resistance, we can use the formula:

R = V / I

where V is the voltage across the unknown resistor, as measured by the voltmeter, and I is the current through the circuit, which can be determined using a current meter or calculated using the known values of the other resistors in the circuit.

A Wheatstone bridge is a circuit that is used to measure an unknown resistance. The circuit is arranged in a diamond pattern, with a known voltage source connected across the middle of the diamond. The unknown resistance is placed in one corner of the diamond, and the other three corners of the diamond contain known resistances, which can be adjusted using a set of rheostats. When the circuit is in balance, the voltmeter connected across the middle of the diamond will read zero.

The principle behind the Wheatstone bridge is that the voltages across the four resistors in the circuit must be equal in order for the circuit to be in balance. This means that the total current flowing through the circuit must be split equally among the four resistors. We can use Ohm’s law (V = IR) to relate the voltage across each resistor to the current flowing through it and the resistance of the resistor.

The formula for the balance condition of a Wheatstone bridge is given by:

V1 / R1 = V2 / R2 = V3 / R3 = V4 / R4

where V1, V2, V3, and V4 are the voltages across the four resistors, and R1, R2, R3, and R4 are the resistances of the four resistors.

To calculate the unknown resistance, we can rearrange the above equation to solve for R3:

R3 = V3 * R4 / V4

where V3 is the voltage across the unknown resistance, as measured by the voltmeter, V4 is the voltage across the resistor in the corner opposite the unknown resistance, and R4 is the resistance of the resistor in the corner opposite the unknown resistance. This equation can be used to calculate the unknown resistance once the circuit is in balance.

The Wheatstone bridge is a circuit used to measure an unknown resistance. The circuit is arranged in a diamond pattern, with a known voltage source connected across the middle of the diamond. The unknown resistance is placed in one corner of the diamond, and the other three corners of the diamond contain known resistances, which can be adjusted using a set of rheostats.

The principle of the Wheatstone bridge is based on the fact that the voltages across the four resistors in the circuit must be equal in order for the circuit to be in balance. This means that the total current flowing through the circuit must be split equally among the four resistors. We can use Ohm’s law (V = IR) to relate the voltage across each resistor to the current flowing through it and the resistance of the resistor.

The formula for the balance condition of a Wheatstone bridge is given by:

(V1 * R2) / R1 = (V2 * R3) / R2 = (V3 * R4) / R3 = (V4 * R1) / R4

where V1, V2, V3, and V4 are the voltages across the four resistors, and R1, R2, R3, and R4 are the resistances of the four resistors.

To calculate the unknown resistance, we can rearrange the above equation to solve for R3:

R3 = (V3 * R4 * R2) / (V4 * R1)

where V3 is the voltage across the unknown resistance, as measured by the voltmeter, V4 is the voltage across the resistor in the corner opposite the unknown resistance, R1 is the resistance of the resistor in the corner adjacent to the unknown resistance, and R2 is the resistance of the resistor in the corner opposite the resistor with resistance R1. This equation can be used to calculate the unknown resistance once the circuit is in balance.