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Resistors in circuits

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Wheatstone bridge

Wheatstone bridge circuit

Wheatstone bridge - there are 4 resistors, R1, R3, R2, and R4 which is a variable resistor. R1 and R3 are in series, and R2 and R4 are in series. R1 and R3 are in parallel to R2 and R4.

The circuit shown above is called a Wheatsone bridge circuit. It can be used to find the resistance of a resistor or it can be used with sensors, such as thermistors, to make measurements.

The variable resistor, R4, is adjusted until the voltmeter reads zero volts. At this point we say that the bridge is balanced.

When a Wheatstone bridge is balanced R1 / R2 = R3 / R4.

If we know the value of three of the resistors in a balanced Wheatstone bridge circuit we can calculate the value of the fourth resistor.

If a Wheatstone bridge is balanced the voltmeter will have a zero reading.

If the bridge is put out of balance by altering the resistance of one of the resistors, a reading will be obtained on the voltmeter. The reading on the voltmeter is proportional to the change in the resistance of the resistor.

Graph of voltage and change in resistance

Graph of voltage and change in resistance - the voltage increases proportionally as the resistance increases

The graph above shows that voltage is proportional to the change in resistance. However it is important to note that this is true only when the change in resistance is very small. Large changes in resistance are not proportional to voltage.

Question

Wheatstone bridge

Wheatstone bridge - there are 4 resistors, R1, R3, R2, and R4 which is a variable resistor. R1 and R3 are in series, and R2 and R4 are in series. R1 and R3 are in parallel to R2 and R4.

The Wheatstone bridge shown above is balanced.

If R1 = 220 Ω, R2 = 550 Ω, and R4 = 1000 Ω , what is the value of R3?

Answer

R1 / R2 = R3 / R4

220 / 550 = R3 / 1000

R3 = (220 × 1000) / 550 Ω

The resistance of R3 is 400 Ω

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