27.13
Wheatstone Bridge
An ohmmeter is a resistance-measuring device. It works by applying a voltage to a resistor of unknown resistance and measuring the current across the…
A Wheatstone bridge is a null measurement device that measures unknown resistance by balancing the potential drop.
It comprises two parallel branches containing four resistors connected by a galvanometer, which acts as a bridge between them. The bridge circuit is connected to a voltage source.
The circuit consists of two known resistors, a variable resistor and an unknown resistor.
The variable resistance is tuned until the galvanometer reads zero.
It implies that the potential at junction points of the central branch is the same, and no current flows through it.
So, the two branches are in a parallel configuration and receive the same potential drop as the voltage source.
Since junction points b and d have the same potential, the potential drop across R1 equals the drop across R3. Similarly, the potential drop across R2 equals the drop across Rx.
Taking the ratio of these two equations yields an expression for the unknown resistor.
Although this method is accurate, uncertainty in known resistance values and inaccurate zero current reading in the galvanometer causes measurement uncertainties.
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Q1: What is a Wheatstone bridge and how does it measure unknown resistance?
A Wheatstone bridge is a null measurement device that measures unknown resistance by balancing potential drops across circuit branches. It comprises two parallel branches with four resistors connected by a galvanometer. The variable resistor is adjusted until the galvanometer reads zero, indicating no current flows through it and the circuit is balanced. This allows calculation of the unknown resistance using the ratio of known resistance values.
Q2: Why is a galvanometer used in a Wheatstone bridge circuit?
A galvanometer acts as a bridge between the two parallel branches of the circuit, detecting when current flow stops. When the galvanometer reads zero deflection, it indicates that junction points have equal potential and no current flows through the bridge. This null condition is essential for accurate resistance measurement, as it allows the unknown resistance to be calculated from the balanced potential drops without drawing current from the circuit.
Q3: How does the Wheatstone bridge achieve balance and what does it mean?
Balance occurs when the variable resistor is tuned until the galvanometer reads zero. At this point, the potential at junction points b and d becomes equal, meaning the potential drop across R1 equals the drop across R3, and the potential drop across R2 equals the drop across Rx. This balanced state indicates no current flows through the galvanometer, allowing accurate calculation of the unknown resistance from the known resistance values.
Q4: What are the advantages of using a Wheatstone bridge over a standard ohmmeter?
A Wheatstone bridge is more accurate than standard ohmmeters because it uses a null measurement technique that draws no current from the circuit. Standard ohmmeters using voltmeters or ammeters alter the voltage applied and current flow, reducing accuracy. The Wheatstone bridge's balanced condition eliminates these measurement errors, providing precise resistance values when the galvanometer shows zero deflection.
Q5: What factors contribute to measurement uncertainty in a Wheatstone bridge?
Two significant factors affect Wheatstone bridge accuracy. First, achieving exactly zero current through the galvanometer is impossible in real circuits; some residual current always flows. Second, uncertainty in the known resistance values directly contributes to uncertainty in calculating the unknown resistance. These combined factors limit the precision of the measurement despite the bridge's superior design compared to standard resistance-measuring devices.
Q6: How does the Wheatstone bridge circuit configuration differ from standard parallel circuits?
The Wheatstone bridge consists of two parallel branches containing four resistors, with a galvanometer connecting the branches as a central bridge element. Unlike standard parallel circuits, the galvanometer acts as a null detector rather than a load. When balanced, both branches receive the same potential drop from the voltage source, and the bridge configuration allows measurement of unknown resistance through the ratio of known resistances.
Q7: What is the mathematical relationship for calculating unknown resistance in a balanced Wheatstone bridge?
When the Wheatstone bridge is balanced, the ratio of potential drops yields an expression for the unknown resistor. Since the potential drop across R1 equals the drop across R3, and the potential drop across R2 equals the drop across Rx, taking the ratio of these equations produces a formula expressing the unknown resistance in terms of the three known resistance values in the circuit.