Master the Basics: Understanding the Wheatstone Bridge

The Wheatstone bridge is a classic circuit used to measure unknown resistances by comparing them to known resistor values. It’s also incredibly useful in detecting small changes in resistance, which is why it’s often found in sensor circuits such as strain gauges or thermistors.

What Is a Wheatstone Bridge?

At its core, a Wheatstone bridge consists of four resistors arranged as two parallel voltage dividers. By applying a voltage to the circuit and then measuring the output at two specific nodes, you can determine an unknown resistance (Rx) based on the relationships between the known resistors and the resulting voltage difference.

How the Wheatstone Bridge Is Arranged

• There are four resistors: R1, R2, R3, and the unknown resistor Rx.
• The resistors are connected so that R1 and R2 form one voltage divider, while R3 and Rx form the other.
• The input voltage V_in is applied to both dividers in parallel.
• The Wheatstone bridge “output” is the voltage difference between the two middle nodes, where R1 meets R2 and where R3 meets Rx.

Single-Ended vs. Differential Measurements

If you measure the voltage of one node with respect to ground, that’s called a single-ended measurement. However, the real power of a Wheatstone bridge is in its differential measurement: measuring the voltage difference between the outputs of the two voltage dividers (the middle nodes), not relative to ground.

Balanced Wheatstone Bridge

The circuit is said to be balanced when the voltage at those two middle nodes is exactly the same, resulting in zero differential voltage (V_out). Mathematically, this happens when:

R1 / R2 = R3 / Rx

In a balanced condition, V_R (the voltage on the right divider) equals V_L (the voltage on the left divider), giving a net output of zero.

Measuring the Unknown Resistance

If Rx increases from its balanced value, V_R will exceed V_L and the output becomes positive. Conversely, if Rx decreases, the output becomes negative. By substituting the voltage divider equations into the relationships for V_L and V_R, you can derive Rx from the measured output voltage.

Rx = R3 * (V_in - V_out) * R2 / (R1 * V_out)   [Example form, exact arrangement may vary]

Don’t be intimidated if the final expression looks complicated. In practice, you usually plug in the numbers from your known resistors (R1, R2, R3), your supply voltage (V_in), and your measured output (V_out).

Real-World Example

Imagine you have a Wheatstone bridge where R1, R2, and R3 are all 10 kΩ, and you apply a 5 V supply (V_in). Let Rx be a 1 kΩ potentiometer you’ve set to an unknown resistance. You measure the differential voltage and find it’s -2.3 V. You can then solve for Rx using the derived formula and your known values.

Why Learn About Wheatstone Bridges?

Even though you may not build a Wheatstone bridge every time you measure a resistor, understanding its operation is crucial. The concept of comparing two voltage dividers and taking differential measurements is a foundation in many sensor and instrumentation circuits. Whether you’re working with strain gauges, temperature sensors, or other precision applications, the Wheatstone bridge is a powerful tool in an electrical engineer’s toolkit.