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.

## AC Bridge

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.

Spesific 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) |

*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 Example

For a better understanding let us review 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 make up**Z**_{x}, and (b) the parallel components that make up**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

__(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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