The Wheatstone Bridge is a circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit.

It is based on Kirchhoff's laws, specifically the voltage law (Kirchhoff's first law) and the current law (Kirchhoff's second law)

• Voltage Law (Kirchhoff's First Law): According to Kirchhoff's voltage law, the sum of the voltages in any closed loop in a circuit is zero.

• In the Wheatstone Bridge, you can consider the loop formed by R₁, R₂, and V₁. Similarly, consider the loop formed by R₃, R₄, and V₂. Applying Kirchhoff's voltage law to these loops:

• For the left loop: −V₁+IR₁−IR₂=0−V₁+IR₁−IR₂=0

  For the right loop: −V₂+IR₃−IR₄=0−V₂+IR₃−IR₄=0

  Here, I is the current flowing through the resistors.

• Current Law (Kirchhoff's Second Law): According to Kirchhoff's current law, the algebraic sum of currents entering and leaving any junction in a network is zero.

• Consider the junction between R₂ and R₃. The current entering the junction is I, and the current leaving the junction is 2I (one going through R₃ and one through R₂).

• Applying Kirchhoff's current law to this junction:

  I−2I=0I−2I=0

  Solving this equation, we find that I = 0, meaning that no current flows through the junction between R₂ and R₃.

For the Wheatstone Bridge to be balanced (meaning no current flows through the galvanometer connected between the junction of R₂ and R₃), the ratio of resistances must be equal:

R₁/R2=R₃/R₄

This is the condition for a balanced Wheatstone Bridge.

The Wheatstone Bridge principle is based on these applications of Kirchhoff's laws, leading to a balanced bridge when the ratio of resistances satisfies the specified condition.

The balanced condition is utilized to measure unknown resistances in practical applications