Question

How do you calculate the voltage and current across elements in a bridge circuit configuration?

Answer 1

In a bridge circuit configuration, the voltage and current across elements can be calculated using principles of Kirchhoff's laws and Ohm's law. Bridge circuits are commonly used for various applications, such as measuring unknown resistance or sensing changes in physical quantities like temperature or strain.

The most common type of bridge circuit is the Wheatstone bridge, which consists of four resistors arranged in a diamond shape. The general configuration of a Wheatstone bridge is as follows:

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      Vcc
       |
       R1
       |
    ----/---- R2
       \
       / \
       \ / R3 (unknown resistor)
       |
    ----/---- R4
       |
       |
      GND


Here's how to calculate the voltage and current across elements in this bridge circuit:

Apply a voltage source (Vcc) across the bridge.

Determine the values of the resistors R1, R2, R3, and R4.

Let's assume the voltage drop across R3 (unknown resistor) is Vx, and the current flowing through R3 is Ix.

Apply Kirchhoff's Voltage Law (KVL) to the closed loop in the circuit (e.g., the loop formed by R1, R2, R3, and R4):

Vcc - Vx - Ix * R4 - Vx = 0

The voltage drop across R1 is the same as the voltage drop across R2, and the voltage drop across R3 is the same as the voltage drop across R4 because they are connected in parallel.

Apply Kirchhoff's Current Law (KCL) to the node between R1, R2, R3, and R4:

Ix + Ix = (Vcc - Vx) / R1 + (Vcc - Vx) / R2

Now you have two equations (one from KVL and one from KCL) with two unknowns (Vx and Ix). Solve these equations to find the values of Vx and Ix.

Once you know Vx and Ix, you can calculate the voltage and current across any element in the circuit.

For example, to calculate the current across R1, use Ohm's law:

Current_R1 = (Vcc - Vx) / R1

Similarly, you can calculate the voltage across any resistor using Ohm's law:

Voltage_Rx = Ix * R3

Please note that this explanation assumes an ideal bridge circuit without any internal resistance, and the resistors are linear and follow Ohm's law. In practical scenarios, factors like wire resistance, temperature coefficients, and non-ideal behavior of components should be considered for accurate measurements.