# Bridge Circuit

A bridge circuit is a topology electrical circuit in which two circuit branches (usually in parallel with each other) are “bridged” with them at some intermediate point by a third branch connected between the first two branches. The bridge was originally developed for laboratory measurement purposes and when it is used one of the intermediate bridging points is often adjustable. Bridge circuits now find many applications, both linear and non-linear, including instrumentation , filtering , and power conversion.

The most famous bridge circuit, the Wheatstone bridge , was invented by Samuel Hunter Christie and popularized by Charles Wheatstone , and is used to measure resistance . It is constructed from four resistors, two known values ​​R 1 and R 3 (see diagram), one whose resistance is to be determined R x , and one which is variable and calibrated R 2 . Two opposite corners are connected to a source of electric current, such as a battery, and a galvanometer .Connected to the other two vertices. The variable resistor is adjusted until the galvanometer reads zero. It is then known that the ratio between the variable resistor and its neighbor R1 is equal to the ratio between the unknown resistor and its neighbor R3, from which the value of the unknown resistor can be calculated.

The Wheatstone bridge has also been generalized to measure impedance in AC circuits and to measure resistance, inductance , capacitance and dissipation factor separately. The variants are known as the Wien bridge , Maxwell bridge and Heaviside bridge (used to measure the effect of mutual inductance).  All are based on the same principle, which is to compare the outputs of two potential dividers sharing a common source .

In power supply design, a bridge circuit or bridge rectifier is an arrangement of diodes or similar devices used to rectify electric current, i.e. to convert it from unknown or alternating polarity to direct current of known polarity. .In some motor controllers, an H-bridge is used to control the direction of the motor .

## Bridge Current Equation

From the figure to the right, the bridge current is defined as I5 . as shown

Finding the Thevenin equivalent circuit that is connected to a bridge load R5 and using an arbitrary current flow I5 , we have;

The Thevenin source ( Vt H ) is equal to;

{\displaystyle ((R2 / (R1 + R2)) - (R4 / (R3 + R4))) * U}
{\displaystyle ((R1 * R2) / (R1 + R2)) + (R3 * R4) / (R3 + R4))}
i = 5{\displaystyle Vth/(Rth+R5)}