3.13. WHEATSTONE BRIDGE

As an application of Kirchhoff’s rules consider the circuit shown in Fig. 3.18, which is called the Wheatstone bridge. The bridge has four resistors R1, R2, R3 and R4. Across one pair of diagonally opposite points (A and C in the figure) a source is connected. This (i.e., AC) is called the battery arm. Between the other two vertices, B and D, a galvanometer G (which is a device to detect currents) is connected. This line, shown as BD in the figure, is called the galvanometer arm.

The Wheatstone bridge is a circuit configuration used to determine the unknown resistance in an electrical circuit. It consists of four resistors arranged in a diamond shape, with a voltage source connected across one diagonal and a galvanometer connected across the other diagonal. The key aspect of the Wheatstone bridge is to achieve a balance point where no current flows through the galvanometer, indicating a specific relationship between the resistances.

Imagine you are trying to balance a scale. The Wheatstone bridge acts like a scale where you add known weights (R1 and R2) on one side and adjust an unknown weight (R4) on the other side until the scale levels out, showing no movement. At this point, you can determine the unknown weight using the weights of the known objects.

For simplicity, we assume that the cell has no internal resistance. In general, there will be currents flowing across all the resistors as well as a current I through G. Of special interest, is the case of a balanced bridge where the resistors are such that I g = 0. We can easily get the balance condition, such that there is no current through G.

In a balanced Wheatstone bridge, the ratio of the resistances is such that there is no current through the galvanometer. Mathematically, this condition is expressed as R1/R2 = R3/R4, meaning that the resistances are in proportion. When this balance is achieved, the bridge can accurately measure the unknown resistance based on the known values.

Consider a balanced seesaw. If both sides of the seesaw have equal weights and are positioned equally, it remains stable and horizontal, just like when the Wheatstone bridge is balanced, ensuring no current flows through the galvanometer.

Thus the condition R1/R2 = R3/R4 relates the four resistors. This last equation relating the four resistors is called the balance condition for the galvanometer to give zero or null deflection. The Wheatstone bridge and its balance condition provide a practical method for determination of an unknown resistance.

To find the unknown resistance R4, one can adjust the known resistors R1 and R2 until the galvanometer shows no deflection. At this point, the condition R1/R2 = R3/R4 holds true, allowing us to calculate the value of R4 based on the other resistances. This method is commonly used in laboratory settings to measure resistance accurately without directly connecting the unknown to a voltage source.

Imagine a tuning fork being used to match the pitch of another fork. By adjusting the tension on the fork, you achieve a perfect match at a certain pitch. Similarly, by adjusting the known resistors in a Wheatstone bridge, you match the conditions until you can determine the unknown resistance accurately.

Let us suppose we have an unknown resistance, which we insert in the fourth arm; R4 is thus not known. Keeping known resistances R1 and R2 in the first and second arm of the bridge, we go on varying R3 till the galvanometer shows a null deflection.

In practical applications, the Wheatstone bridge is widely used in measuring unknown resistances, calibrating measuring instruments, and even in temperature measurement through resistance thermometers. A common method involves inserting an unknown resistance in the fourth position of the bridge and adjusting the other resistors until the galvanometer zeroes out, allowing for precise determination of the unknown value.

Think of a smartwatch that measures your heart rate. Just as the device calibrates certain parameters automatically for accuracy, the Wheatstone bridge calibrates resistors to provide accurate readings of unknown resistances in electric circuits.

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