Question

How are electrical parameters measured using a Wheatstone bridge?

Answer 1

A Wheatstone bridge is a type of electrical circuit used to measure an unknown electrical resistance by balancing two legs of the bridge with known resistances. It is widely used for accurate resistance measurements and can also be adapted to measure other electrical parameters such as voltage and current.

The basic Wheatstone bridge consists of four resistors arranged in a diamond shape, with a voltage source connected across one diagonal and a galvanometer (a sensitive current-measuring device) connected across the other diagonal. The two sides of the bridge are often referred to as the "ratio arms" and the "balance arms."

Here's how electrical parameters can be measured using a Wheatstone bridge:

Resistance Measurement:
The most common application of a Wheatstone bridge is to measure an unknown resistance (R_x) by adjusting the known resistances (R_1, R_2, and R_3) until the bridge is balanced. When the bridge is balanced, no current flows through the galvanometer, indicating that the voltage drop across both sides of the bridge is equal.

The bridge equation for resistance measurement is:
R_x = (R_2 / R_1) * R_3

By varying the known resistances (R_1, R_2, and R_3) and monitoring the galvanometer for a null deflection, you can find the value of the unknown resistance (R_x).

Voltage Measurement:
A Wheatstone bridge can also be used to measure unknown voltages. In this case, a known resistance is used in one arm, and the unknown voltage is connected to the ratio arms of the bridge. The balance is achieved by adjusting a variable resistance (often referred to as the "null detector" or "galvanometer resistance") in the balance arm.

The voltage measurement equation is:
V_x = (V_s * R_2) / R_1

Where:
V_x = unknown voltage
V_s = voltage of the source
R_1 = known resistance in one arm
R_2 = resistance in the other arm adjusted until the bridge is balanced

By adjusting the resistance R_2 in the bridge until the galvanometer shows null deflection, you can determine the value of the unknown voltage V_x.

Current Measurement:
A Wheatstone bridge can be adapted to measure an unknown current (I_x) by converting it to a voltage using a known resistor. The current to be measured is passed through the known resistor, and the voltage developed across it is measured using the bridge.

The current measurement equation is:
I_x = V_s / (R_1 * R_2)

Where:
I_x = unknown current
V_s = voltage of the source
R_1 = known resistance
R_2 = resistance in the bridge adjusted to balance the circuit

By adjusting the resistance R_2 in the bridge until the galvanometer shows null deflection, you can calculate the value of the unknown current I_x.

In all cases, achieving a balanced bridge (where the galvanometer shows no deflection) is crucial to obtaining accurate measurements.

Answer 2

The Wheatstone bridge is a widely used circuit for measuring electrical parameters, especially resistance. It is named after Samuel Hunter Christie and Sir Charles Wheatstone, who popularized the configuration in the 19th century. The primary use of the Wheatstone bridge is to accurately determine an unknown electrical resistance by comparing it to known resistances.

The basic components of a Wheatstone bridge circuit include four resistors arranged in a diamond shape, with a voltage source applied across two opposite corners, and the remaining two corners used for measurement. The configuration typically consists of the following elements:

Unknown Resistor (Rx): This is the electrical parameter that you want to measure. It could be a resistor, a sensor with a known resistance-temperature relationship, or any other component with a resistance that needs to be determined.

Three Known Resistors (R1, R2, and R3): These are precisely known resistors, which act as reference elements. The accuracy of these resistors directly impacts the measurement accuracy of the unknown resistor.

Voltage Source: A stable and known voltage source (V) is connected across the bridge.

Galvanometer (G): A sensitive current-measuring device, such as a galvanometer, is connected between two corners of the bridge. The galvanometer detects the presence or absence of a current through its coils.

The circuit is balanced when the current through the galvanometer is zero, indicating that the potential difference between the two measurement points is zero. This condition is achieved when the ratio of the resistances on one side of the bridge equals the ratio on the other side. Mathematically, this can be expressed as:

(R1 / R2) = (Rx / R3)

From this equation, the unknown resistance (Rx) can be calculated as:

Rx = (R1 * R3) / R2

To measure the unknown resistance, you would adjust the known resistors R1, R2, and R3 until the galvanometer shows zero current. At that point, the resistance values are balanced, and you can substitute the known resistor values into the formula to calculate the unknown resistance (Rx).

It's important to note that Wheatstone bridges can also be used to measure other electrical parameters, such as capacitance and inductance, by replacing the resistors with capacitors or inductors and adjusting the bridge configuration accordingly.