An ac bridge circuit is one of the simple application of RLC ac circuits along with phase shifter.

This bridge circuit is used in measuring the inductance L of an inductor or the capacitance C of a capacitor.

Make sure to read what is ac circuit first.

## AC Bridge Circuit

It is similar in form to the Wheatstone bridge for measuring an unknown resistance. To measure L and C, however, an ac source is required as well as an ac meter instead of the galvanometer.

The ac meter may be a sensitive ac ammeter or voltmeter.

(3) |

This is the balanced equation for the ac bridge.

Specific ac bridges for measuring L and C are drawn in Figure.(2), where L_{x} and C_{x} are the unknown inductance and capacitance to be measured while L_{s} and C_{s} are a standard inductance and capacitance (the values of which are known to great precision).

In each case, two resistors, R_{1} and R_{2}, are varied until the ac meter reads zero. Then the bridge is balanced. From Equation.(3), we get

(5) |

Notice that the balancing of the ac bridges in Figure.(2) does not depend on the frequency *f* of the ac source since *f* does not appear in the relationships in Equations.(4) and (5).

Figure 2. Spesific ac bridges: (a) for measuring L, (b) for measuring C |

## AC Bridge Circuit Example

For a better understanding let us review the example below :

1. The ac bridge circuit of Figure.(1) balances when **Z**_{1} is a 1 kΩ resistor, **Z**_{2} is a 4.2 kΩ resistor, **Z**_{3} is a parallel combination of a 1.5 MΩ resistor and a 12 pF capacitor, and *f* = 2kHz. Find: (a) the series components that makeup **Z**_{x}, and (b) the parallel components that makeup **Z**_{x}.

__Solution :__

From Equation.(3),

__(a)__ Assuming that **Z**_{x} is made up of series components, we substitute Equations.(1.2) and (1.3) in (1.1) and get

(1.4) |

Equating the real and imaginary parts yields R_{x} = 5.993 MΩ and a capacitive reactance

__(b)__ **Z**_{x} remains the same as in Equation.(1.4) but R_{x} and X_{x} are in parallel. Assuming an RC parallel combination,

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