# Wien’s Bridge

**The Wien’s bridge use in AC circuits for determining the value of unknown frequency**. The bridge measures the frequencies from 100Hz to 100kHz. The accuracy of the bridges lies between 0.1 to 0.5 percent. The bridge is used for various other applications like capacitance measurement, harmonic distortion analyser and in the HF frequency oscillator.

The Wien’s bridge is frequency sensitive. Thereby, it is difficult to obtain the balance point in it. The input supply voltage is not purely sinusoidal, and they have some harmonics. The harmonics of the supply voltage disturbs the balance condition of the bridge. To overcome this problem the filter is used in the bridge. The filter connects in series with the null detector.

When the bridge is in the balanced condition, the potential of the node B and C are equal, i.e., the V_{1} = V_{2} and V_{3} = V_{4} The phase and the magnitude of V_{3} = I_{1}R_{3} and V_{4} = I_{2}R_{4} are equal, and they are overlapping each other. The current I_{1} flowing through the arm BD and the current I_{2} flowing through R_{4} is also in phase along with the I_{1}R_{3} and I_{2}R_{4}.

The total voltage drop across the arm AC is equal to the sum of the voltage drop I_{2}R_{2} across the resistance R_{2} and the capacitive drop I_{2}/wC_{2} across the capacitance C_{2}. When the bridge is in a balanced condition, the voltage V_{1} and V_{2} both are equals in magnitude and phase.

The phase of the voltage V_{1} and the voltage drop I_{R}R_{1} across the arms R_{1} is also same. The resistance R_{1} is in the same phase as that of the voltage V_{1}. The phasor sum of V_{1} and V_{3} or V_{2} and V_{4} will give the resultant supply voltage.

On equating the real part,

On comparing the imaginary part,

By substituting the value of ω = 2πf,

The slider of the resistance R_{1} and R_{2} mechanically connect to each other. So that, the R_{1} = R_{2} obtains.